Choose the tool for the job.

MySQL is a fridge:
Good storage. Good price. Needs something else like PHP to pull stuff from
the fridge and serve it.

Access is a restaruant.
It has a good fridge, but also a great interface for serving up the food to
local patrons. However, the Access interface does not work well beyond a
local-area-network.

Oracle is a warehouse.
You buy it, along with the trucks to get things in and out and the
maintenance people to manage it if you need something that size.

    Well, this is an Access specific group, so I suspect at least
90%, if not more, responses will say Access is the best choice...

    Access is, as I recall, described as a "file server" database.
In its simplest form, all processing is done on the client machine with
the contents of the database file being passed across the network.

    Oracle, MySQL, Firebird (Open Source evolution of Interbase),
"MaxDB by MySQL" (Open Source evolution of SAP-DB) are all
"client-server" databases. Processing tends to be performed on the
database server machine.

    Access/JET [JET is the actual database engine -- Access is a
GUI-builder front-end for it] (and M$ MSDE [a lightweight "desktop"
version of SQL Server]) is limited to a total database size of 2Gbytes.
The others aren't so limited -- MySQL's limit is 2 (or 4?) GB per table
for MyISAM tables; InnoDB tables create files as needed to avoid a
limit. The others also use custom multi-file handling.

    Many web sites are using MySQL. There are fat books on using
PHP/MySQL for web work; Python has API modules for a number of
databases, including MySQL. Zope has MySQL adapters.

    MySQL has had, for a long time, a reputation for being, if not
/the/, one of the fastest RDBMs out there. Some of this speed is from
using the MyISAM tables, which do not support transactional controls.
InnoDB tables, Firebird, Oracle, MaxDB, MSDE/SQL Server all are
transactional systems.

    Cost? Well, if you meet the requirements of the licenses, and
don't need paid support, I suspect anything but Oracle, Access/JET,
MSDE, and SQL Server are all available for download (well, MSDE is also
available, but I'm not sure of license for use other than a home
network).

    Since web work doesn't really use Access forms/reports, all you
really are using is the JET engine. Might as well use MSDE -- same
database size limit, but transactional, scalable to SQL Server if you
later need that ability, and client/server style.

    For a web site... I'd probably use (in decreasing preference)
MySQL, Firebird, MaxDB.

    Oh, there is also PostgreSQL -- I understand a native Windows
version is in the works...

    Ah... And I've read some announcement that Ingres is going to
free download. (Of course, there is the minor historical stuff that
Ingres started as a University project, was spawned off to be a
commercial product, the university then started Postgres, and later
grafted an SQL interface onto it -- I'm sure that Ingres has also added
SQL now).