I can highly recommend libGDX as a game engine. It has good performance and a good set of features, is under active development and there are lots of tutorials on the web.
As Jimmt said, I would also recommend going with the Actor/Stage approach (called Scene2D) assuming that you are creating a 2D game. It makes drawing and transforming 2D objects (Actors) much easier as you do not need to worry about rendering them out to the screen yourself. This is taken care of by Scene2D.
To get started, download the LibGDX Setup Tool from
http://www.aurelienribon.com/blog/2012/04/new-app-libgdx-project-setup/. This enables you to setup a basic libGDX template project in Eclipse within a few minutes. Next, simply start developing a game. Whenever you get stuck and don't know how to do something, check out the tutorials and examples at
http://libgdx.badlogicgames.com/documentation.html or post a question in the forum at
http://badlogicgames.com/forum/.
There is a little learning curve, but it is worth the effort. And keep in mind that your game is multiplatform too! Even if you plan on just targetting Android for you game, this is a real benefit because you can run and debug on your PC, which is way quicker than on a mobile device.
