For better security, how would I move bitcoin from my Coinbase Wallet and Vault to a hardware wallet like Trezor?
Generate an address on the hardware wallet. Then log in to your web wallet account and send all your coins to that address. That's all.
I suggest using Jaxx wallet. It is available on most platforms and mobile.
Simply open the app, it will generate a new wallet, and you can use your coinbase wallet to send bitcoins to the new address.
Coinbase is not a good place to keep bitcoins.