Coinbase isn't a wallet. It's an app to interact with the exchange.
I have used quite a few mentioned here (Mycelium, Breadwallet, Blockchain). I personally recommend Copay. They have a very simple to use interface and are great for new users.
Mycelium is also good for more advanced users as it has more functionality. Breadwallet is ok too. I found Blockchain annoying as I had to have network connectivity to see my balance etc. This was frustrating if I was on a plane (or somewhere without network connectivity) and wanted to double check the size of a recent transaction or my current balance.