Well coinomi on Android is great because it has a built in exchange. You hold the private keys to the wallets. Speaking of which... When or if you get a wallet and it tells you to write down a phrase... Write it down at least 4 times and keep it. That's the key, if it's lost then so are the coins. The key is usually 24 word phrase, thus very very hard to hack.

I would suggest getting a phone wallet... Since you're less likely statistically to destroy your phone over a hard drive loss. If you're an apple person, jaxx is not a bad choice. The wallets also give you qr code access and have such low fees you will be disgusted with what the exchanges charge you, especially coinbase.

The other reason to pull off the exchange is because with changing legislation the exchanges have started thinking about sending 1099s on gains. If they can't track what you have/sold/spent then that makes it tougher for them to try and tax you. I'm only against the taxing because for years they won't acknowledge cryptocurrency but they will still try to tax you? Seems crooked to me