If you suspect your computer has been compromised, then even disconnecting from the Internet temporarily won't necessarily protect you. You really want to be on a completely clean system before you generate any private keys.
Transferring BTC from your Coinbase wallet to your paper wallet will just be a matter of sending coins to an address associated with your paper wallet. Without using or exposing your private key, you can verify that the coins have gotten where they were going by looking at the balance of that address on blockexplorer.com or blockchain.info.
When you want to spend those BTC someday, you'll probably end up importing the key you used for your paper wallet into local wallet software or an online wallet. As far as I know, that's the easiest way to go. Somebody who has more experience than I do with paper wallets may be able to correct me here.
