If you want something that has both BTC and ETH, then you have Coinomi which is probably the most used one, Eidoo, and Enjin. Unlike the options suggested aboveo, these wallets are not open source though, and even though there have been no reports about a scam, use them at your own risk.
It looks like Coinomi will fit the best.
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?