1. If you're going to deposit a big amounts, deposit them in small portions as exchanges have deposit (technical) issues so If for some reason the deposit didn't go through, you won't lose everything.

2. Always withdraw your funds as soon as you finish trading, exchanges can close your account and enforce KYC/AML verification without prior notice.

3. Always take a backup of your 2FA. An exchange may not be able to help you If you lose it.

And no, just because an exchange is charging higher fees, doesn't mean that It's more secure or safer.