You said:
It makes more sense that God requires our faith, at least initially, or it would undermine the command for there being a Great Commission, going into all the world, preaching the gospel, and missionary work. God can increase our faith afterwards.
Why is it so hard to understand that the Gospel must be preached indiscriminately because one cannot know who has been prepared for the Word. The Great Commission is for the "general" proclamation of the Gospel but the one proclaiming cannot know who it is that has been Regenerated and as such can "hear" the message. Thus, the message is only "effectual" to those who are regenerated.
John 8:43 Why do ye not understand my speech? Even because ye cannot hear my word. (Unregenerate)
Mat_13:16 But blessed are your eyes, for they see; and your ears, for they hear. (Regenerate)
You said:
God is patient, not wanting anyone to perish, but all to come to repentance.
2Pe 3:9 The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
Who are the "to us-ward" or the "toward us"? All of mankind? Certainly not. If that was true then all mankind would be saved. If God is not willing that any should perish, then non would perish - for who can stand against His will? Obviously then, the "toward us" refers to God's Elect.
You said:
"God requires faith, but He only gives faith as a gift to certain people. Meanwhile, He is desiring that everyone repents, but for those who weren't given faith their repentance is futile, ineffective, and they're going to perish anyway even though God doesn't want them to perish; however, He selects who perishes and who is saved by the gift of faith."
Let's break this down:
"God requires faith, but He only gives faith as a gift to certain people.
Faith is an outgrowth of Regeneration. Since Regeneration is the Sovereign work of the Spirit and the recipient is "passive" in it's reception, this act makes the recipient "able" to "hear" the Gospel. Saving faith is an outgrowth of this new nature and as such can be called a gift.
Meanwhile, He is desiring that everyone repents, but for those who weren't given faith their repentance is futile, ineffective, and they're going to perish anyway even though God doesn't want them to perish
As mentioned above, this is not the proper interpretation of 2 Pet. 3:9. From John Gill:
but is longsuffering to us-ward: not to all the individuals of human nature, for the persons intended by us are manifestly distinguished from "some men" in the text, and from scoffers, mocking at the promise of Christ's coming, in the context, 2Pe_3:3; and are expressly called beloved, 2Pe_3:1; and God's longsuffering towards them is their salvation, 2Pe_3:15, nor is it true of all men, that God is not willing that any of them should perish, and that everyone of them should come to repentance, since many of them do perish in their sins, and do not come to repentance, which would not be the case, if his determining will was otherwise; besides, a society or company of men are designed, to which the apostle himself belonged, and of which he was a part; and who are described, in his epistles, as the elect of God, called out of darkness, into marvelous light, and having obtained like precious faith with the apostles; and must be understood either of God's elect among the Jews; [edit] or of the elect in general, whether among Jews or Gentiles, upon whom the Lord waits to be gracious, and whose longsuffering issues in their conversion and salvation. And upon account of these the Lord stays his coming till their number is complete in the effectual calling; and for their sakes he is longsuffering to others, and bears with a wicked world, with the idolatry, superstition, heresy, profaneness, and impiety, with which it abounds; but when the last man that belongs to that number is called, he will quickly descend in flames of fire, and burn the world, and the wicked in it, and take his chosen ones to himself.
The Alexandrian copy reads, "for you", or your sakes; and so the Vulgate Latin, Syriac, and Ethiopic versions. A passage somewhat like to this is met with in a book of the Jews (f), esteemed by them very ancient.
He selects who perishes and who is saved by the gift of faith."
NO. He selected who perishes and who is saved by Election. He then Predestinated those who were elected to salvation. Election is an essential part of God's Grace and guarantees "faith" upon Regeneration.