libgdx is a good base to use for android game development. It has lots of things that make 2D game development easier, such as sprite and animation classes, easy input detection etc.
It's also got support for running c++ stuff for more cpu intensive tasks (physics etc.) which is what I think its using for its Box2D integration.
Its not a complete game engine, more of a base to build your own on top of, but I prefer that as it gives me the freedom to code in a way that I'm comfortable with.
As for books, I think the creator of libgdx has written a book for android game development for beginners, it was featured on gamedev.net recently and has good reviews. Could be worth checking out.
Libgdx - http://code.google.com/p/libgdx/
Beginning Android Games - http://www.gamedev.net/page/books/index.html/_/programming-1/platform-specific-16/mobile-37/beginning-android-games-r1405