There's no doubt that if you use ASP, you want to go for SQL Server 7/2000. Contains a hell of a lot of features, including Triggers/Stored Procedures/and Text Indexing. SQL Server 2000 now can be used along side XML. It has a good learning curve, and the interface makes it a lot easier to grasp all the RDBMS concepts.

MySQL can't handle Stored Procedures or triggers yet, and it functions along the command line (like Oracle). (Although there are some GUIs out there for it.) MySQL is a good place to start though for PHP. It's free and reliable for personal apps. It's all pretty easy to use. From what I hear, PostgreSQL is only available on Unix/Linux types of machines, but there's a way around it using Cygwin.

If you want to start with an EASY database, I suggest using Access with ASP, unless you can afford SQL Server 2000 or Oracle 8i/9i. If you have any other questions, ask away.

Cheers