“If God chooses individuals for regeneration with no concern for anything regarding that individual’s beliefs, choices, thoughts, character or actions then for what conceivable reason does God choose one person over another?”
The exact reasons we are never told. It is simply a fact. All that the Lord reveals to us on the matter is that it is according to “His grace and purpose” or His “pleasure” that He decides to pluck His own peculiar people from the fire.
God has always chosen, according to His own purpose, a peculiar people for Himself. He chose the seed of Abraham instead of any other seed in the world to accomplish His purposes and be His people. He never revealed Himself to the Greeks in any special way, or the Vikings or anyone else, giving them Prophets and special care and protection. This was to the Jews only, and not to any other.
Yes God does choose for His purposes and His pleasure, but both of those involve reason and reason always must have some basis in His knowledge. God does not make any choice at random or for no reason or without any knowledge. Any decision He might make in choosing particular individuals must take into account at least one piece of knowledge He has of that individual. The Biblical answer is clearly that He takes into account who has faith in His Son as the only determining factor.
Since faith has no merit, then basing His decison on the individual's faith in Christ preserve salvation by grace alone.