We can talk Access v. mysql v. Postgre v. whatever all day long.
Personally, I like mysql because most of the websites I develop run LAMP, Access is fine for small sites with little traffic and I've found it very useful for small company internal projects, but first, I think the more pertinent questions are:
What is the database going to be used for? Saying you want a db is a little vague, I've had a good number of clients ask for a database without knowing what that means or for what their going to use it.
What platform is the site running?
How much traffic?
What's your coding background?
These will lead you to your answer. Good luck.
Erik
http://www.lutenegger.com