Well, you can make anything up on your own, why not make a Peoples Yellow Pages thing, this is the first thing I did when I started

Make it so people can add there own info, make it so people can view, and make another file for admins, so they can edit/delete entries.
IMO this really will help you understand, because it deals with 3 major sql functions. "Insert, Retrieve, Remove, and Update". This again is good for a first php & mysql script.
I would suggest that you do this first, so you can get familier with mysql and php, before moving on to more harder things.
Anyways good luck
-Arunan