He is to accept whatever suffering comes upon him.  Christianity will cost something, and Christians are to pay the price of it without grumbling and without regret. 

He is to do the work of an evangelist. In spite of the demand for conviction and rebuke, Christians are essentially the bringers of good news. If they insist on discipline and self-denial, it is because an even greater happiness may be attained than common and easily bought pleasures can bring. 

He is to leave no act of service unfulfilled. Christians should have only one ambition – to be of use to the Church of which they are a part and the society in which they live. The opportunity not to be missed is not that of a cheap profit but that of being of service to God, to the Church and to other people. ~Barclay Commentary

Now to the other commentaries.

First, we will go to the general commentaries and move to the specific. Again Paul is speaking minister to minister but clearly all these admonitions speak, in principles and concepts, to all

Let us begin with the Matthew Henry Main. We are breaking into commentary covering the first eight verses.

5. He must watch in all things. “Seek an opportunity of doing them a kindness; let no fair occasion slip, through thy negligence. Watch to thy work; watch against the temptations of Satan, by which thou mayest be diverted from it; watch over the souls of those who are committed to thy charge.”

Note: All firstfruits must seek opportunities in all they do for every element, concept and principle they hold in the salvation process.

6. He must count upon afflictions, and endure them, make the best of them. Kakopathe¯son, endure patiently. “Be not discouraged by the difficulties thou meetest with, but bear them with an evenness of spirit. Inure thyself to hardships.”

Note: Every word in this point applies to every firstfruit.

7. He must remember his office, and discharge its duties: Do the work of an evangelist. The office of the evangelist was, as the apostles' deputies, to water the churches that they planted. They were not settled pastors, but for some time resided in, and presided over, the churches that the apostles had planted, till they were settled under a standing ministry. This was Timothy's work.

Note: Clearly we do not have any evangelists or apostles among us at the moment, but we all have duties and we must apply ourselves to those duties in the same way an evangelist would apply himself to his duties.

8. He must fulfil his ministry: Make full proof of it. It was a great trust that was reposed in him, and therefore he must answer it, and perform all the parts of his office with diligence and care.

Note: And so must we.

Observe,

(1.) A minister must expect afflictions in the faithful discharge of his duty.

(2.) He must endure them patiently, like a Christian hero.

(3.) These must not discourage him in his work, for he must do his work, and fulfil his ministry.

(4.) The best way to make full proof of our ministry is to fulfil it, to fill it up in all its parts with proper work. ~Matthew Henry Main

Now something from the Biblical Illustrator on the phrase, "But watch thou in all things."

But watch thou in all things.

1. But watch thou. The apostasy and looseness of the times we live in must make us the more watchful. Their [the world] falls must be our fears; their levity must quicken us to constancy, and their negligence must quicken our diligence in keeping the watch of the Lord.

2. Good men desire the Church’s good after their departure. Paul is dying, yet he commands Timothy to improve his talents for the Church’s good when himself was dead. Moses, before he dies, prays the Lord to set up a fit ruler instead . Wicked men care not what becomes of the world, when they are dead and gone let heaven and earth come together, and all be in confusion, they care not. But good men have public spirits.

3. As all persons, so ministers especially must watch. The devil hath a special spite at them; he commands his agents, as the king of Aram did his followers, to fight neither with small nor great, but against the king of Israel; so he bends all his strength against the ministers of Israel.

(1) The better the man, the more watchful must he be. The pirate sets on the laden ship, and the thief upon the wealthiest traveller. But we must watch as pastors too, and discover wolves that would destroy the flock.

(2) We must watch at all times.

(a) In prosperity, as pigeons when they fare best fear most.

(b) Watch in adversity, the devil is busy then in laying snares, as the fowler doth for birds in frosty weather.

(3) In all places, in public and private, at home and abroad; the world is full of snares.

(4) Watch in all things, so runs the text.

(5) Watch against all sins. We carry about us a proneness to all sin.

(6) Watch over all thy senses; stop thine ears; make a covenant with thine eyes (Job 31:1). Set a watch before thy mouth. The whole soul is out of order, and therefore we must set a guard upon all its faculties.

Quoted verse:
Job 31:1
I made a covenant with mine eyes; why then should I think upon a maid?

4. Ministers especially must be hardy men. We are called soldiers, shepherds, watchmen, husbandmen, all which must endure summer’s heat and winter’s frost.

(1) We must endure hardship in our preparatory studies; we must give up ourselves to reading, study and prayer.

(2) He must endure hardship in the actual performance of his duty.

(3) Most properly and genuinely this hardship in the text consists in a patient undergoing of those injuries and oppositions which we must expect from an ungrateful world.

(4) The Lord Himself sometimes is pleased to exercise us, and to inure us to hardship, that we may be the fitter for His service. But let us, like good soldiers of Christ, endure hardship—

(a) Patiently.
(b) Courageously.
(c) Constantly.

5. The ministry is a work. The sweat of the brow is nothing to that of the brain; besides the dangers we are liable to for our work’s sake.

6. Do the work or service of an evangelist. Observe, ministers are servants, and their office is service.

7. Of an evangelist. Observe, ministers must preach the gospel. We must publish the glad tidings of a Saviour (what in us lieth to all the world); this is to do the work of an evangelist, viz., soundly and sincerely to publish the gospel.

8. Make full proof of thy ministry. Ministers must fully and faithfully discharge all the duties of their calling. ~Biblical Illustrator

Note: and so should all of us.

Now to the Matthew Henry Concise

People will turn away from the truth, they will grow weary of the plain gospel of Christ, they will be greedy of fables, and take pleasure in them. People do so when they will not endure that preaching which is searching, plain, and to the purpose. Those who love souls must be ever watchful, must venture and bear all the painful effects of their faithfulness, and take all opportunities of making known the pure gospel. ~Matthew Henry Concise

Take a look at the Jamieson, Fausset, Brown:

I am no longer here to withstand these things; be thou a worthy successor of me, no longer depending on me for counsel, but thine own master, and swimming without the corks; follow my steps, inherit their result, and the honor of their end.

Watch thou — literally, “with the wakefulness of one sober.”

In all things — on all occasions and under all circumstances (Titus 2:7).

Quoted verse:
Titus 2:7
In all things shewing thyself a pattern of good works: in doctrine shewing uncorruptness, gravity, sincerity,

Endure affliction — suffer hardships .

Evangelist — a missionary bishop preacher, and teacher.

Make full proof of — fulfil in all its requirements, leaving nothing undone (Acts 12:25; Romans 15:19; Colossians 4:17). ~Jamieson, Fausset, Brown

Quoted verses:
Acts 12:25
And Barnabas and Saul returned from Jerusalem, when they had fulfilled their ministry, and took with them John, whose surname was Mark.

Romans 15:19
Through mighty signs and wonders, by the power of the Spirit of God; so that from Jerusalem, and round about unto Illyricum, I have fully preached the gospel of Christ.

Colossians 4:17
And say to Archippus, Take heed to the ministry which thou hast received in the Lord, that thou fulfil it.

Now to the specific commentaries:

The commas in this verse easily break it out in four parts:

1] But watch thou in all things.
2] Endure afflictions.
3] Do the work of an evangelist.
4] Make full proof of thy ministry.

1] But watch thou in all things.

But watch thou in all things - Be vigilant against error and against sin, and faithful in the performance of duty; See the Matthew 25:13 note; 1 Corinthians 16:13 note. ~Barnes Notes

Quoted verses:
Matthew 25:13
Watch therefore, for ye know neither the day nor the hour wherein the Son of man cometh.

1 Corinthians 16:13
Watch ye, stand fast in the faith, quit you like men, be strong.

But watch thou in all things - It is possible to be overtaken in a fault, to neglect one’s duty, and to lose one’s soul. Watching unto prayer prevents all these evils. ~Adam Clarke

But watch thou in all things - Relating to himself, his doctrine, and conversation; and to others, to feed the flock of God under his care, to know the state of them, and care for them; to give the time of night, and notice of approaching danger, and see the laws of Christ put in execution; either in allusion to shepherds, who watch over their flocks night and day; or to watchmen that are upon the walls of cities, or go about them; or to the priests and Levites in the temple: ~John Gill

2] Endure afflictions.

Endure afflictions - See the notes at 2 Timothy 2:3. The Greek word here is the same which is there rendered “endure hardness.” ~Barnes Notes

Quoted verse
2 Timothy 2:3 [See Lesson]
Thou therefore endure hardness, as a good soldier of Jesus Christ.

Endure afflictions - Let no sufferings affright thee; nor let the dread of them either cause thee to abandon the truth, or relax in thy zeal for the salvation of men. ~Adam Clarke

Endure afflictions - the Alexandrian copy adds, "as a good soldier of Jesus Christ", as in 2 Timothy 2:3 [mentioned above] meaning reproaches and persecutions for the sake of the Gospel, from without, and all trials and exercises from within, through the infirmities and ill conduct of the saints themselves; all which are to be endured patiently, cheerfully, and courageously; so as not to be moved by them to desist from the work of the ministry: ~John Gill

3] Do the work of an evangelist.

Do the work of an evangelist - On the word “evangelist,” see the notes on Acts 21:8. The phrase here means, “do the work of preaching the gospel,” or of one appointed to proclaim the glad tidings of salvation. This is the proper business of all ministers, whatever other rank they may maintain. Whether it was ever regarded as the proper duty of a separate class of men to do this, see the notes on Ephesians 4:11. ~Barnes Notes

Quoted verses:
Acts 21:8
And the next day we that were of Paul's company departed, and came unto Caesarea: and we entered into the house of Philip the evangelist, which was one of the seven; and abode with him.

Ephesians 4:11
And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;

Do the work of an evangelist - That is: Preach Christ crucified for the sins of the whole world; for this, and this alone, is doing the work of an evangelist, or preacher of the glad tidings of peace and salvation by Christ. An angel from God was first sent to do the work of an evangelist, and how did he do it? Behold, said he, I bring you good tidings of great joy. Behold, I evangelize unto you great joy, which shall be to all people; to you is born a Savior. Those who do not proclaim Christ as having tasted death for every man, and who do not implicitly show that every human soul may be saved, do not perform the work of evangelists; they, God help them! limit the Holy One of Israel. Yet, as far as they preach the truth in sincerity, so far God acknowledges and blesses them and their labors; they do a part of the work, but not the whole. ~Adam Clarke

Do the work of an evangelist - which may design either an officer, then in the church, distinct from apostles and prophets on the one hand, and pastors and teachers on the other; and was below the former, and above the latter; and was aiding and assisting to the apostles, and such an one Timothy may be thought to be: or it may intend a preacher of the Gospel in common; and to do the work of such an one is not to read lectures of morality, or to preach up justification and salvation by the works of the law; or to mix law and Gospel together, and confound them both; but to preach peace, pardon, righteousness, life, and salvation alone by Jesus Christ, and through the free grace of God: ~John Gill

4] Make full proof of thy ministry.

Make full proof of thy ministry - Margin, “fulfill;” compare the notes at Romans 14:5. The word here used denotes, properly, to bear or bring fully; then to persuade fully; and then to make fully assured of, to give full proof of. The meaning here seems to be, “to furnish full evidence of what is the design of the Christian ministry, and of what it is adapted to accomplish,” by the faithful performance of all its duties. Timothy was so to discharge the duties of his office as to furnish “a fair illustration” of what the ministry could do, and thus to show the wisdom of the Saviour in its institution. This should be the aim of all the ministers of the gospel. Each one should resolve, by the blessing of God, that the ministry, in his hands, shall be allowed, “by a fair trial,” to show to the utmost what it is adapted to do for the welfare of mankind. ~Barnes Notes

Quoted verse:
Romans 14:5
One man esteemeth one day above another: another esteemeth every day alike. Let every man be fully persuaded in his own mind.

Make full proof of thy ministry - Push all thy principles to their utmost power of activity; carry them on to all their consequences; and try what God will do for thee, and by thee. Neglect no part of thy sacred function; perform faithfully all the duties of which it is composed; and do God’s work in his own way and in his own spirit. ~Adam Clarke

Make full proof of thy ministry - the work of the ministry, which lies in preaching the Gospel, and administering ordinances, and doing all the duties belonging to it, which is to fulfil it, or discharge it; and which gives full proof of a man's being a true and faithful minister of the word; particularly when he diligently and constantly attends to his work; seeks not his own things, but the things of Christ; cheerfully and patiently suffers for Christ and his Gospel, and lives an agreeable life and conversation. ~John Gill

Recap:

Admonitions for both minister and member.

---Be vigilant against error and sin.
---Be faithful to the performance of your duties
---Ministers: preach true doctrine. Members: receive and hold true doctrine.

---Do not be fearful of sufferings.
---Do not allow sufferings and afflictions to cause you to abandon truth.
---Do not allow sufferings and afflictions to weaken your fervency, diligence and zeal.

---Be a good soldier of Jesus Christ. Do not be shaken by reproaches and persecution from without or from ill conduct of saint within.
---All ministry and members: Do the work of an evangelist, meaning be conformed to the image of Christ, be His example and invoke all fervency, diligence and zeal.
---Ministers and members: make full proof of the ministry. That is, be a full illustration of the gospel, the principles of God and the elements of the salvation process.

---Push all the principles of God to their utmost power of activity; carry them to their promised consequence [conclusion].
---Do God's work in the way He would do it.
---Neglect no part of your sacred function. Perform it faithfully.

These are the lessons of verse 5.