Best Gamepad Controller for Note 3?

[xLightning]

Hey, I was wondering what would be a good gamepad to play games on the Note 3? I'm mostly looking forward to playing emulators such as the NES, SNES, Sega Genesis/Megadrive and so on.

Would a PS3 controller work if my phone isn't rooted? Or should I get something like MOGA Pro if many games are compatible with it?

I've once tried a PS4 controller via Bluetooth but the input lag was horrendous. Looking for something lag free if available.

Thanks in advance.