Is this the proper way to remove a user account?

Try removing the account from Settings app > Accounts > Family & other users > locate the account > click Remove. Confirm with Yes.

This is more advanced and effective way of removing the account.

Using the steps you mentioned—Control Panel > All Control Panel Items > User Accounts > Manage Accounts > Change an Account—allows you to select and delete a user account. However, whether all files and folders associated with that account are removed depends on how you perform the deletion.

If you choose to delete the account and delete files, all files and folders associated with that user account will be permanently removed from the system.