What resolution should my game be?

I’m finding it quite hard to adapt to soo many different resolutions, I’ve decided to provide multiple APK’s to the google play store, but the AppStore has no option to provide Multiple APK’s.

Can you guys suggest some tutorials that stretch the gameplay to fill the screen, I do not care if it distorts.

Also, how do you guys go about this process?

u target ratio not resolution aka 16:9 16:10 5:4 etc, also here is a list for you:
(u target 16:9)
http://hwstats.unity3d.com/mobile/

What GUI system do you use? uGUI? NGUI?

In all GUI system, you can set anchors, and all content will scale according to it.

For uGUI: Rect Transform - Unity Official Tutorials - YouTube