Help to find correct game engine

Hi everyone. I am experienced web dev and I want to try creating games for Android, iOS platforms. I know PHP, JS, some Java.

For beginning I'd like to create some maze game with many levels, different modes to play. After it I want to create some simple word game or some 2D runner.

I need to choose right game engine.

For now I have next options:

1. Libgdx
2. Unity
3. Corona SDK

So, my questions are:

1. What game engine should I choose for beginning?
2. What game engine should I choose for maze game?
3. What game engine should I choose for word game and simple 2D runner?

Thanks!