I believe it would be best to try and incorporate the full-blown arsenal of a LAMP developer. Your project should focus on a little bit of the following aspects (as this seems to be the way of the web to date):
PHP
One of the most frequently used features of a website is a user registration system. This covers many important aspects such as security, sessions, cookies (if you use remember me functionality), database interaction, and form handling.
MySQL
A user registration system will tie in with a database of your choice. MySQL is the obvious choice but there are plenty of alternatives. You should familiarize yourself with querying and retrieving records from the database as well as structuring your database, indexing, and optimizing queries.
Javascript/AJAX
An added bonus. You should familiarize yourself with javascript. My framework of choice happens to be jQuery as it easily abstracts some fairly difficult tasks into more mundane, managable code on your end. You could make AJAX requests for a forgot password feature to pass an email address and automatically send an email to the user and respond with a success or error response.