I'll go a little broader than the immediate stick problem, but hopefully it helps others new to FGs. Others already mentioned it to various degrees, but you can play effectively on pad/stick/keyboard/hitbox/etc. The important thing is choosing the one that's most comfortable for you and having something of sufficient quality (so that it doesn't break, or so that it can read multiple inputs, etc)
I play on a pad and actually prefer it to stick, though for a number of people, it's the other way around. I spent a lot of time between stick and a ps2 pad in the MVC2 arcade days - my college had a cab. But I bring that up because it kinda brings me to my the main point I wanted to mention.
Consider where you plan on doing most of your playing when you decide on the type of controller to use. Pad was fine when I was playing on ps2 at home with friends. But if I wanted to hang in the arcades when I was on campus, or when me and friends went to Family Fun Arcade, I had to learn how to play stick, period. For MVC3, because I went back to playing pad (PS3), I was limited as far as competition. I could only battle folks on my console because I didnt own a converter.
For skullgirls, to make a longer story short, I'm able to use a PS4 pad on both the PC version and the PS3 version and it works like a dream. However, a dual modded 360/PS3 stick wouldn't really have much to worry about. They could jump between platforms with little worry.
Now if you don't really care about all that and mainly intend on doing netplay from your specific version, then obviously these issues are less important.
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Lastly, for those that do choose a traditional pad instead of the 6-button fight pads, I'd encourage you to give claw-style grip a shot. It's a nice inbetween for pad and stick play with some nice benefits.
my button config is as follows: square=LP, triangle=MP, X=LK, circle=MK, L1=HP, R1=HK.
Instead of using my thumbs for the right face buttons, I tap the face buttons with my index finger (for X); middle finger (for Square); ring finger (for Triangle and Circle). I can easily input 'throw' (middle finger + Index finger), get easy two-button dashes (middle + ring), and then easily do PP/KK specials as needed (middle + ring again, across the "top" and "bottom" rows).
I still use my left thumb for the dpad, but I have Fierce punch mapped to L1 (I use my left index finger) and Heavy kick mapped to R1 (I use my right ring finger). It may sound a bit odd, but remember that when it comes to chaining, Heavy/Fierce are the end of the line, generally speaking. Finger gymnastics arent really occurring, as most of my time is on the face, with occasional shoulder taps.
So what do you have to give up in exchange for easy access to each button a la an arcade stick? Well, it takes a while to learn the most comfortable way to rest the controller on your thigh.... -_-