I only have access to a shared drive (no database server). If I put a MS Access Database on the shared drive and tried to access it from a Java program on at most three or so different PCs at the one time, how well would that work?
All RDBMS's are designed to be multiuser. That is with the exception of MS Access which is notoriously bad at handling anything more than 1 user. You should however be able to use it well enough if your purpose is just to have a convenient DB for development. If you plan to use it for a production system however, I'd strongly advise using something else (MySQL is the obvious freely avaliable DB platform).