Smash Bros was one of the first fighting games I played as a kid too and it was awesome. I was pretty good with pretty much any character in the original, though I mostly used Mario, Link, Samus, and Captain Falcon. I got Melee and had a blast too, and ended up using the same characters with some new ones like Dr. Mario and Young Link. I eventually eneded up getting Soul Calibur 2 just because it had Link, but I liked it too, it was a game I never played. Link became my main, but later on in team battles, Mitsurugi, and Cassandra became my partners with Link. I was good with Leon too.
As for Marvel vs. Capcom 3, I always have Captain America with me, as for the rest, it's either Chun Li, Dante, or Zero. On Tatsunoko vs. Capcom, I always use Zero and Batsu, sometimes I switch one with Jun the Swan, but I try to use as many characters as I could to see how they play and find ones that I'm good with. But really, despite that, we usually just want to use our favorite characters.
On Injustice, Batman is my main and the character I use the most, plus I'm more familiar with him. I know all his special moves, and know how to pull off a few hits before using his super move, it gives a bit more damage but's satisfying to watch. I like how fighting games give you so many characters, they have different fighting styles, but they give you so many to find one you're familiar with.