Is it a good idea to move this into a wallet? Any suggestions on how to do this or what tools to use (I don't have a wallet or any other tools setup).
Or is this something I shouldn't be concerned about for some reason?
Coinbase is probably at much less risk than these other companies, as they make money entirely off fees, not lending coins out, and have weathered more bear markets than any other exchange at this point (that I'm aware of at least), so they're probably the safest place to keep it if you're going to keep it not in your own wallet, but still, not your keys, not your bitcoin, and all that.
Can’t get hacked and lose your coins.
Not your keys not your coins!