Coinbase is a nice online wallet/exchange of bitcoin. However, you will not be able to totally controlling your coins since Coinbase is handling your private keys.
Please read their terms & conditions before using Coinbase.
The no gambling / casino thing from coinbase isnt that shocking. I think they are just doing there best to make sure they operate within the law. Its Unlikely that they are monitoring ever transaction from every address but to be safe you should probably get a local wallet. I recommend Multibit HD since it uses a online blockchain and you dont have wait forever to dowload it like the QT wallet. They probably aren't checking and added that in the TOS to comply with US laws.