I disagree,
Coinbase, never never never store your currency on an exchange. You don't have control of your private key. Therefore, your coins are not in your control. Therefore you don't own your coins, coinbase does. They only have a loan out to you for that value. If they go under, your coins are gone. This is basic basic basic stuff.

Then, you left of Jaxx. A multi-coin, HD wallet supported on multiple platforms, iOS, Android, Mac, Windows, Linux. I use Jaxx. I'm happy with them. Support is very responsive and friendly, having emailed them numerous times with issues.