MySQL is one of the best database applications available for Unix servers -
it is definitely the most popular.
Some alternatives:
1) Change to a host that provides Windows servers (if you wish to use
Access)
2) Build your own database using flat text files, and write your own code
to address them.
3) Find a Shopping Cart application that uses its own "built in" database -
for example:
http://www.nightmedia.net/shop/index.html (note-this is not easy to
customise, and is not secure)
3) Hardcode the prices into your pages