PPSSPP is compatible with almost any recent Android phone, and almost any reasonably new controller for PC. This page lists some things that have been tested to work. More products will be added soon.
The Nvidia Shield is the king of gaming Android devices. Unfortunately it's not very future proof as it does not support OpenGL ES 3.0.
The Nexus 5 and Nexus 6 are good phones to run PPSSPP on, along with most major "flagship" phones.
The Samsung Galaxy S devices work pretty well.
Any controller that is usable on Windows will work, those that support XInput will autoconfigure, too.