You store your bitcoins in wallets. Coinbase is a web based wallet. Hardware wallets are the most secure. Here are a few.
Trezor was the first one to come out and is the standard, at least for now. Keepkey just purchased the software wallet Multibit. They will be integrating their Chrome app functions, which includes altcoin exchanges through shapeshift.com. I use coinbase to buy my bitcoins. I then send them to one of my hardware wallets.
Trezor also has a web based password manager that is accessed using their hardware wallet. It doesn't have the flashier functions of Lastpass etc, but it's probably the most secure.