For me, it was Mario in 64 and Brawl and Dr. Mario in Melee. For 64 and Brawl, I picked him because I was a die-hard Mario fan. In Melee, I unlocked a few characters after playing Classic and Vs. Mode and stuff (as a bunch of characters, don't quite remember them) and saw Doc, and said, "Dr. Mario? This'll be interesting." So I played Mario and Doc and thought Doc was better, because he was stronger but didn't have a spike. I'm okay with all characters in all three games now, but if I entered a tournament, I'd probably pick Doc or Mario (depending on what game).
In Brawl though, I'm trying to get better with characters I don't usually play, like Olimar, Lucario, ROB, and Fox. So I might pick Fox in a tournament, but knowing it's Brawl, I'd probably pick Metaknight. :/
I realized right off the bat that MK was awesome, so I played him a lot, but I didn't want to be cheap, so I moved on.
EDIT: Also, a friend from school recently got 3rd in a tournament using Kirby. He is also good with Wolf. I'm saying this to build on the fact that I don't know whether I'll ever enter a tournament, I'm young and I'll probably be laughed at because of my appearance. Unless I'm absolutely sure not everyone is going to pick MK, Snake, or Dedede (and they so are), or unless I'm sure I'm good enough, I'll probably hone my skills against CPUs or something, considering my Wifi sucks.