Point # 1 (vs. 1-2) Right living: praying biblically

Christians are to pray for all sorts of individuals . . . .

a) specifically, those in authority
b) with a view to civil peace, in an environment where the gospel might advance, and where Christians live lives of godliness and holiness.

Point # 2 (vs. 3-6) The right doctrine informing the right living:

a) God is the saviour who desires all people to be saved and come to a knowledge of the truth of the gospel – therefore, Christians pray for the salvation of those in authority.
b) That God would have all people be saved is a necessary corollary of the truth of monotheism and of the provision of only one mediator - the man Christ Jesus
c) The extent of the mediator’s ransom is “for all people.” This has been witnessed to at the proper time.

Point # 3 (v.7) Paul’s own career in proclaiming the gospel to Gentiles - not just Jews - bears out the reality of the universal scope of God’s WILL to save.