MySql is a suitable choice for a J2EE application. I have not used it
personally so
I don't want to endorse it but I know that a fair amount of successful J2EE
projects
use MySql.

Generally speaking access  is unsuitable for any large appliation. Its primary
intention is for a single user database (your cookbook for instance). Access
may
work fine during development and perform horribly in production once multiple
users
are hitting it.

Check the user manual on the number of rows. I'm pretty sure the number of rows
limit is very high. However this is not entirely myth. Although you can save
any
number of rows  in an access database performance degrades substantially as the
size
increases. In particular performance with the Microsoft DAO driver is extremely
problematic (the exact number of rows is a function of available memory) and
most
other drivers available are built on top of this driver. Thus you might be able
to
import 10 million rows with access but then not use them efficiently in your
application with jdbc.