Any recommendation for an iPhone game controller?

I’d like to try Street Fighter, but I don’t think I manage to play very well with onscreen buttons.
So, has anyone tried one of those gamepads or game controllers? Any preferences? Are they at the same time with Apple TV and iPad?
I’ve also heard that some Sony Playstation controllers are capable to connect via Bluetooth with iOS devices. Does anyone know anything about that?

Thanks in advance for any help, folks.

Cheers,

Xavier