You can use Unity, just be aware that it is very big.

Unity is WONDERFUL if you have a small team with experienced programmers, modelers, and animators. If it is just you, know that you will be doing more than just programming, you will also need to fill all the other roles of game development.

It can be very overwhelming for a beginner. You certainly can do it, and there are many programmer-only games developed using Unity, just know going in that the system is large and is designed for the needs of professional team.

As was written above, there are many options available to you. Some are more beginner-friendly than others.

Here's a great tutorial you should check out any time you want info on getting started in mobile games:

http://bit.ly/1c4NfgB

^ Dunno why my comment's getting so many downvotes. This is yet another of the endless posts on gamedev every single day asking the same question that has been asked here. It's not even a good question.

"But I wanna know what the guys on gamedev think!" Well here, I looked it up on gamedev for you.

http://www.gamedev.net/index.php?s=91066940eef8fce03e6859dbf8065824&app=googlecse#gsc.tab=0&gsc.q='where to start mobile games'

Seriously, to everyone reading this, the next time you want to know where to start with anything, be it programming, cooking or mud wrestling, just look it up.

One thing I'd avoid at all costs is writing your game directly in Java or Obj-C. While those are the "official" ways to program on Android and iOS, doing so will lock your code to one platform, and you don't want that. (Which is awesomely ironic for Java when you think about it. )

The easiest way would be to use a readily made cross-platform game engine. Since you mentioned having experience in C#, you might be interested in Unity 3D. While I'm personally not a fan of writing games that depend on an proprietary engine I don't have the source code for, doing so will spare you the entire gory engine programming and get you to the meat of the game a lot faster, and Unity is more than good enough for Unity. (It's actually packed with features that 99% of the indies don't even have the means to use.)

If you have simple graphical needs and would like to get your hands dirty, you might also opt to write the game in portable C++ and use Java/Obj-C only to wrap the platform's API. It's a lot harder but it's very rewarding when you see the end of it. I really wish both Apple and Google made C++ a 1st class language like Microsoft, but I guess that helping developers to port their games to the competition is against their best interests.

Then there are middle grounds like MonoGame or OGRE for mobiles. Basically you have the graphic rendering library but not an entire game engine. I dunno how good or stable those libraries are though, I haven't tried them.