Electrum is a safe and easy to use wallet. It does not download the full blockchain, but uses a network of specialized servers that index the blockchain. This safes a lot of storage space. Besides, it is fully open source.
Exodus is also a good wallet that lets you control your private keys.
Thank you :)
What happens to one's crypto when his computer crashes( in case of web wallet) or Phone gets stolen (in case of app)
Some Bitcoins are lost forever.
A backup of the Bitcoin wallet is very important of course :)