I use Coinbase but with verification and all this stuff.. Do the Coinbase Android wallet need also documents verification if i want store there only cryptocurrencies?
For basic stuff (send and receive Bitcoin on small amount), you don't need to verify your identity.
But the private key/seed is owned by Coinbase and they could freeze your account if you send receive Bitcoin from suspicious/illegal address (such as dark net market and casino) since they comply with US regulation.
Frankly, i wouldn't recommend Coinbase (except for buy/sell bitcoin) to newcomers at it will give them wrong idea about Bitcoin.
Coinomi is best choice if you don't mind closed-source application. You also can check
https://bitcoin.org/en/choose-your-wallet if you think all recommendation doesn't suit for newcomers.