A web wallet is one such wallet. You do not need to use any additional applications to save it. It is much safer. In my opinion, web wallet is much better than mobile wallet. Using it does not require a separate space. Hopefully the wallet will expand further in the future.
You think web wallet is safe? You do know that most of the web wallets don't give you access to your own private keys. This means that once you send your coins to that wallet, no longer are the owner of the coins! Even if they do allow you to access your private keys, they might also have access to it which still bring in the doubt of security. Don't forget, web wallets can be hacked easily if they get access to your username and password. Also I doubt you would store your keys anywhere since you think you don't need to do anything "additional".
You better start learning how to keep your wallets safe.