Welcome!
Most here use stick I believe, but I'm sure there are a few pad warriors too. Try a stick by all means if you never have before (probably best to borrow one if possible before investing on a decent stick) - you could find it improves your game, but then again it may not. Ultimately just go with what feels comfortable for you.
My tip is pick one character and focus on him/her. Go through all the trials and spend time in training mode perfecting your basic 'bread and butter' combos. After that see if you can get a friend to play you locally (if not in person then someone who is close enough that the online connection will be good) and ideally someone who maybe has a bit more experience than you and willing to use lots of different characters against you (so you can learn the match ups). Trying to get those combos in a real game against a live opponent, while trying to remember basic things like blocking, spacing, and anti-airs, is overwhelming at first so just concentrate on the basic control of space when you start playing against others, rather than on flashy combos and lots of them. And don't just hit buttons for the hell of hit. If unsure, wait and defend. Go for guaranteed damage, basic combos at the most when you see an opening.
Finally, join PSN* SSFIV gafchat (add one of the regulars like the_log_ride or EraldoCoil and they'll invite you) and get some games in - it's all fun. There's no secret other than to play against real people a lot.
* There are peeps here on XBL too if you don't have a PS3, though not as many from what I know.
Good luck.