I cannot say anything about coinbase, but according to me Binance is the best exchange.
As you asked how you could choose thr right exchange, then i will advise that go by the nost trusted ones.
A exchange should be capable to pay you your funds instantly and i think Binance is expert on it.
Secondly the exchanges should help their clients instantly in case of emergency and that happens with Binance too.
So according to me Binance can be a good choice.
I do always suggest on using up of Electrum instead when you do withdraw or pulling or storing up your funds for long term.
Exchange wallets aren't advisable and in talk with reputation and accessibility and good UI/UX then I would really choose Binance
among other exchanger even they do suffer some issue in the past but they are doing pretty good atm.