I've been messing with crypto long enough to know how this goes and my coins are already in a local wallet.

Coinbase had a good run but don't be stupid. Crypto exchanges aren't insured like consumer checking accounts are in the US and when they're gone they're gone. Geth isn't hard to set up for most of us, it took me about 20 minutes to have it up and running after not using a local wallet for nearly a decade.

Remember to write down your password (I can't emphasize that enough. I'd be retired by now if I had done that with the wallet I made in 2011) and back up your wallet. I keep mine in git.