Then I was reading up and read that I shouldn't store my coins on exchanges because if they're hacked you could lose everything.
Right. You shouldn't keep your bitcoin on an exchange and that's not only due to possibility of getting hacked.
You shouldn't keep your bitcoin on an exchange, because in this way, you give them full control over your bitcoin and they can freeze your fund at any time for any reason.
It's recommended to use a non-custodial wallet or a hardware wallet.