Choose mobile wallet. I would recommend you to use Mycelium on your Android. Mycelium is a lightweight wallet that gives you full control of your private key (it requires you to back up your private key). Online wallet usually does not. Look blockchain.info online wallet for example, AFAIK you can't access your private key, only some backup phrases or something. If you don't own the address private key = you don't own the Bitcoin in that address. Storing your BTC in online wallet also means giving someone else (the online wallet service provider) control of your Bitcoin.

So, stick to desktop or mobile wallet that give you (and only you) full control of your Bitcoins.