In regards to safety..... They all say their wallets are safe and maybe they are. I would however have sleepless nights with all my coins lying in a phone wallet. I never keep more than around 0.5 in my phone wallet. Rest is kept offline and moved to the phone as required.
Yes, don't keep more on your phone wallet than you expect to need. Use it the same way like you would use an ordinary wallet.
Even if the wallet implementation might be safe, your phone may still be unsafe because of the platform itself. Also it might be stolen. Offline storage is the only resonably safe way to store larger amounts of Bitcoin.
Apart from that, mycelium is a good choice.