Looking for Controller for Android for PPSSPP

[ShadowfoxEX]

I'm looking for recommendations for a controller I can use with my phone to use with PPSSPP. The one I have is pretty cheap and crummy and now broken.

The issues I had with the one I bought and would like to avoid:
- The trigger buttons and thumbstick had a bit of a deadzone right out of the box. I could play, but the feedback was terrible and I couldnt exactly move as I'd have liked.
- Response time had a bit of a lag. I couldnt time it, but I assume the bluetooth version was a bit outdated, but that alone couldnt let me play fighters.
- Buttons were tiny. I dont mind this as much, but I measured them and it's about 6 mm, and it's not comfortable to press over and over again
- Back/Select button was the same back button for a phone. I dont know if this is every controller, but I worked select out by binding it to another button

As for things I'd like
- A Method to hold the phone
- Wireless/Bluetooth
- Built in battery, not one that you buy and replace