I don't know your web development skills, but you can give a CMS a shot. Be aware, however, that because you're just learning PHP (not to mention the first time you develop a CMS) you might make some crucial mistakes in creating it. However, you just want a learning experience, right? Anyways, there's lots of documentation on the net for CMS and PHP, so I'm sure you can do it. In any case, here are a few ideas for web applications you can try:
Project Manager
E-Mail (Like Yahoo)
Address Book
Shopping Cart
Monopoly / Dungeons and Dragon Game Clone
Snippet Manager
Forum
Portal
Blog
Inventory Control
Invoice Management
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a.k.a inscissor
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since Feb 2002