Coinbase is an exchange with wallet capacity. You should never use exchanges and online wallets anyways.
I also recommend mycelium, just don't hold big amounts on it!
Cheers!
Why not? I use coinbase as my regular day to day wallet in my PC. I think it is quite fast and reputable.
It's an online wallet! You don't have control over your funds. If something happens to the Coinbase, if someone hacks them or whatever, all your money will be gone. If you use it, at least don't keep big amounts in online wallets.
On the other side, I don't like Coinbase, and many serious bitcoiners don't either. Do a research, Google a bit. Coinbase complies with every damn requirement that government puts in front of them. In their TOS it's stated that they have right to transmit your person info to the governmental officers. They might be as well sending all of their personal customers data to the NSA.
Coinbase goes directly against the all of the decentralization that Bitcoin brings.
Again I repeat, with very small day to day amounts you will be OK.