The Matthew Henry Commentaries, completed by Benjamin Andrews Atkinson, 1 Tim 2:1-6:

II. As a reason why we should in our prayers concern ourselves for all men, he shows God’s love to mankind in general, v. 4. 1. One reason why all men are to be prayed for is because there is one God, and that God bears a good will to all mankind. There is one God (v. 5), and one only, there is no other, there can be no other, for there can be but one infinite. This one God will have all men to be saved; he desires not the death and destruction of any (Ezek. xxxiii. 11), but the welfare and salvation of all. Not that he has decreed the salvation of all. for then all men would be saved ; but he has a good will to the salvation of all, and none perish but by their own fault, Matt. xxiii. 37. He will have all to be saved, and to come to the knowledge of the truth, to be saved in the way that he has appointed and not otherwise. It concerns us to get the know ledge of the truth, because that is the way to be saved; Christ is the way and the truth, and so he is the life. 2. There is one Mediator, and that Mediator gave himself a ransom for all. As the mercy of God extends itself to all his works, so the mediation of Christ extends itself thus far to all the children of men that he paid a price sufficient for the salvation of all mankind; he brought mankind to stand upon new terms with God, so that they are not now under the law as a covenant of works, but as a rule of life. They are under grace; not under the covenant of innocence, but under a new covenant: He gave himself a ransom. Observe, The death of Christ was a ransom, a counter-price. We deserved to have died. Christ died for us, to save us from death and hell; he gave himself a ransom voluntarily, a ransom for all; so that all mankind are put in a better condition than that of devils. He died to work out a common salvation: in order hereunto, he put himself into the office of Mediator between God and man. A mediator supposes a controversy. Sin had made a quarrel between us and God; Jesus Christ is a Mediator who undertakes to make peace, to bring God and man together, in the nature of an umpire or arbitrator, a days-man who lays his hand upon us both, Job ix. 33. He is a ransom that was to be testified in due time; that is in the Old-Testament times, his sufferings and the glory that should follow were spoken of as things to be revealed in the last times, 1 Pet. i. 10,11. And they are accordingly revealed, Paul himself having been ordained a preacher and an apostle, to publish to Gentiles the glad tidings of redemption led salvation by Jesus Christ. This doctrine of Christ’s mediation Paul was entrusted  preach to every creature, Mark xvi. 15. He was appointed to be a teacher of the Gentiles ; besides his general call to the apostleship, he was commissioned particularly to preach to the Gentiles, in faith and truth, or faithfully and truly. Note, (1.) It is good and acceptable in the sight of God our Savior that we pray for kings and for all men, and also that we lead a peaceable and quiet life ; and this is a very good reason why we should do the one as well as the other. (2.) God has a good will to the salvation of all; so that it is not so much the want of a will in God to save them as it is a want of will in themselves to be saved in God’s way. Here our blessed Lord charges the fault : You will not come unto me that you may have life, John v. 40. I would have gathered you, and you would not. (3.) Those who are saved must come to the knowledge of the truth, for this is God’s appointed way to save sinners. Without the cannot be good; if we do not know the truth, we cannot be ruled b it. (4.) It is observable that the unity of God is asserted, and joined with the unity of the Mediator; and the church of Rome might as well maintain a plurality of gods as a plurality of mediators. (5.) He that is a Mediator in the New-Testament sense, gave himself a ransom. Vain then is the pretense of the Romanists that there is but one Mediator of satisfaction, but many of intercession; for, according to Paul, Christ’s giving himself a ransom was a necessary part of the Mediator’s office ; and indeed this lays the foundation for his intercession. (6.) Paul was ordained a minister, to declare this to the Gentiles, that Christ is the one Mediator between God and men, who gave himself a ransom for all. This is the substance of which all ministers are to preach, to the end of the world; and Paul magnified his office, as he was the apostle of the Gentiles, Rom. xi. 13. (7.) Ministers must preach the truth, what they apprehend to be so, and they must believe it themselves ; they are, like our apostle, to preach in faith and verity, and they must also be faithful and trusty.

Supplementum:

The Matthew Henry Commentaries, completed by Benjamin Andrews Atkinson, 1 Timothy 4:10:

2. Those who labor and suffer reproach in the service of God and the work of religion may depend upon the living God that they shall not lose by it. Let this encourage them, We trust in the living God. The consideration of this, that the God who has undertaken to be our pay-master is the living God, who does himself live for ever and is the fountain of life to all who serve him, should encourage us in all our services and in all our sufferings for him, especially considering that he is the Savior of all men. (1.) By his providences he protects the persons, and prolongs the lives, of the children of men. (2.) He has a general good-will to the eternal salvation of all men thus far that he is not willing that any should perish, but that all should come to repentance. He desires not the death of sinners; he is thus far the Savior of all men that none are left in the same desperate condition that fallen angels are in. Now, if he be thus the Savior of all men, we may hence infer that much more he will be the rewarder of those who seek and serve him; if he has such a good-will for all his creatures, much more will he provide well for those who are new creatures, who are born again. He is the Savior of all men, but especially of those that believe; and the salvation he has in store for those that believe is sufficient to recompense them for all their services and sufferings. Here we see, [1.] The life of a Christian is a life of labor and suffering: We labor and suffer. [2.] The best we can expect to suffer in the present life is reproach for our well-doing, for our work of faith and labor of love. [3.] True Christians trust in the living God; for cursed is the man that trusts in man, or in any but the living God; and those that trust in him shall never be ashamed. Trust in him at all times. [4.] God is the general Savior of all men, as he has put them into a salvable state; but he is in a particular manner the Saviour of true believers; there is then a general and a special redemption. [Credit to Tony for the find.]

From Matthew Henry:

1) 1. We must pray for the whole world of mankind, the lost world and thus we must honour all men, and according to our capacity do good to all men.

We pray, as we are taught, for all men, believing that this is good and acceptable in the sight of God our Savior, who will have all men to be saved, and to come unto the knowledge of the truth, and of Jesus Christ, who gave himself a ransom forall. Matthew Henry, “Method of Prayer,” in The Complete Works of Matthew Henry, (Grand Rapids Michigan: Baker, 1978), 2:48