I know next to nothing about Access,
but I love MySQL. It's fast and easy.
There was a benchmark run a while ago
(wish I could remember the reference)
wherein MySQL beat everything else
hands down except Microsoft SQL Server
IF SQL Server was running on a finely
tuned MS-only platform. MySQL doesn't
have stored  procedures yet (supposed
to come out in version 5) but I don't
know if Access has those either or if
you need them. My experience is that
you usually don't unless you're running
a high-demand system. Besides, MySQL
is default on almost every commercial
Web account, so it makes sense to
develop Web applications using it.