No bitcoin wallet is safe online.
Every time i buy bitcoin i quickly send it to my desktop wallet. That way i control my wallet.
So the safest is:
Bitcoin Core Wallet -
https://bitcoin.org/en/download
Online wallets:
1.
https://bitpay.com/
1.
https://blockchain.info/
2.
https://localbitcoins.com/
I use those 4. Have't had any problem with them.
Coinbase is a bad company. They have bad service and will block your account if you transfer too much money in and out. They will ask you too much personal information and except you to pay taxes on your income.