If I withdraw all my money from a paper wallet, but don't end up spending the whole balance, should I create a new paper wallet and send that remaining balance to it as opposed to the old wallet?
For security and privacy reasons I would advise you create a new paper wallet and send that remaining balance to it. For privacy so that you don't reuse the address and for security so that you don't reveal your public key on the blockchain when spending the first transaction. Until funds in a wallet are spent, only the hash of the public key is visible on the blockchain. Afterward funds are spent, the public key gets revealed. It is not such a big issue but more secure not to reveal the public key especially in terms of quantum security.