Why not coinbase? I hear that phone wallets seem better to privately own bitcoin. Blockchain.info or Coinbase.com are good, you can purchase bitcoins directly from Coinbase too and they will instantly apear in your wallet!
In this case it sounds like he's waiting for a transaction to an existing address. You have to import your details elsewhere to receive it. Opening a new wallet won't help.
Some people don't like the idea of a company controlling their private keys. I wouldn't be keen on the idea either but Coinbase is a solid choice for many.
Yes, it's not a good idea don't keep the private key.
ok some company are "strong" but a loss or an hacking could disrupt years of savings.
why not store by yourself the private key?