Honestly , There are tons of mobile engines out there that can help you get the job done. Knowing that it's huge and vast, I find Unity as your best bet. It makes implementing the menu easier and plus you can make menus pretty easily. In addition to that, It also now offers 2D support which I think helps you achieve your goal pretty easily with free mobile deployment.
Alternatives to Unity are :
Corona - Which you have already tried
App Game Kit - Which is also amazing : http://www.appgamekit.com/
I find those engines the three best engines for the game your looking to build since it's easy and needs some fast mobile game development engines.
You can also try some WYISWYG programming environments such as Scirra's Construct 2.
Hope you find that useful.