When I start my present computer (Windows XP), I have to choose whether to be the Administrator or myself. I have not had to do so before. What would be the result of deleting the Administrator from the log in screen?
you can't do that. only an administrator can delete accounts, and an administrator cannot delete their own account, only another administrator can do that (so in essence there must always be an administrator)
So, is your own account an 'administrator' account? If so, you should be ok to delete the administrator account if you don't use it.
If you're not an 'administrator' then you'll need to login under the administrator account and make your own account an 'administrator', before doing the above.