I am beginning to use GPG for email encryption. If I use 
gpg --edit-key [keyID] to change the passphrase, what files will this affect? Will it only affect my private key, and thus I only need to rebackup this key? Will it leave my public key and the revocation certificate alone, or will these need to be regenerated and then distributed and stored, respectively? 
Your PGP private key is encrypted at rest. Altering the passphrase re-encrypts your private key, but it does not affect the actual private key itself. Your passphrase is used to encrypt your private key. From How PGP Works:


  PGP uses a passphrase to encrypt your private key on your machine. Your private key is encrypted on your disk using a hash of your passphrase as the secret key. You use the passphrase to decrypt and use your private key.


When you change your passphrase, the protection around your private key has been altered, but the key itself has not. Consequently, the matching public key is still valid, since its corresponding private key is unchanged.

You can back up your newly encrypted private key, since the encryption protection around the key has changed, but the key itself is unchanged.
