It all depends…
It seems like most “serious” players would advice to get a stick, but it all depends. Personally, I bought a SF4 pad for $20 at Best Buy. If you are having i$$ues, a pad would be a nice investment, and a step above the shitty 360 controller. Your game will get much better and your inputs a lot more accurate with a fight pad.
Now, I can play with a stick, but I play much better with a pad. The way I hold the stick (palm up, joystick between 2nd and 3rd finger) hurts my hand. I guess I could hold the joystick some other way; I could, but it just doesnt feel right. I think, even if I could afford a stick, I would rather stick with the pad.
Now that is just me. Most pros play with sticks, and I’d say whatever brings you the best results, be it stick or pad.