Copay is no longer recommended as their parent company, Bitpay, have been trying to switch their users to 2X without their knowledge or consent. Regardless of your feelings about 2X, users should have complete control over their coins and not be forced to chance if they don't want.
Check out this link for some recommended wallets:
https://bitcoin.org/en/wallets/mobile/android/Personally, I have used Electrum and Mycelium, and would recommend either.
You "back up" a wallet by writing down the 24 word recovery phase that will be given to you when you first set up the wallet. Those 24 words allows anybody with them to recovery your wallet - so keep them safe and secure!