I've never even been to a convention yet, to be honest, and I've never seriously thought about attempting a cosplay.
Though since I am a bigger guy, I'd want to choose a character that matches my stature without going with the "Batman after his golden years" kinda thing. The Heavy from TF2 could be pretty cool.
If I'm not talking about video games, Choji from Shippuden was always one that came to mind (I guess he is sorta in games) and I would love to do Al from Fullmetal Alchemist, but I think that would be a bit much if it were my first ever cosplay...