Well, you'll probably hear this a lot but you can't go wrong with MySQL. As long as you don't need foreign keys, stored procedures or transaction support (and most web sites really don't), this will do the job.
I've had very good luck with it. One recommendation - if you go with MySQL, get the O'Reilly book "MySQL & mSQL" - a little bit of reading will save you a lot of trouble, and it provides a good reference MySQL's tools, SQL statements and datatypes supported, and several programming APIs.
