Bachus, I think you have partly answered your question when you say "you just take a style that sounds good with the song". (and also what John said).
That is an important part of this topic, to do what feels good to you, and that will most times feel good to others.
There is no "one size fits all" in this case, many styles and sounds can give a good result.
Example, i have three different registrations saved for Fly Me To The Moon. One is slow Latin, another is mid big band, and another is fast jazz trio, (piano drums and bass),all tweaked to my liking, and I enjoy playing all three, depending on my mood at the time.

Ray