if you want to "store" your bitcoins in some wallet and not touch it for some time then you should choose a safer option such as an offline wallet (cold storage) or at least keep a wallet on your PC instead of your phone since a cell phone can easily be lost or stolen since you carry it around while your PC is less in danger.
as for Mycelium, it is an open source wallet that has been around for quite some time now so it should be safer.
and for the 0 balance thing read this:
https://bitcointalk.org/index.php?topic=5091798.msg0#newThanks for the zero balance thread.
I would still consider to store my bitcoins on my smartphone since I always keep the backup of the private key in a password protected file and store it both on my smartphone and my PC. So I guess it is safe to store the bitcoins in a smartphone wallet.