MySQL vs. Microsoft Access
MS Access Vs MySQL


MS Access works only on Windows whereas MySQL works on almost all platforms.
MS Access does not support Partitioning feature whereas MySQL has composite, Range partitioning support.
MySQL is opensource so no cost involved. 
Performance in MySQL is way better than MS Access 
MS Access database is more suitable for desktop use with a small number of users accessing it simultaneously. One reason you might choose to use Microsoft Access over SQL Server is for compatibility/sharing. You might need to email someone a copy of your database. People are more likely to have Access on their desktop computer than SQL Server. 
Security - MS Access is limited to security in terms of user-name/password on the database. Where as MySQL is much more secured and you can configured it with SSL support. 
MySQL is the most famous or rather more loved amongst the professional folks because of it's multiple choice in custom storage engines. You can have custom storage engines developed in MySQL based on your requirements or choose amongst the inbuilt ones
Actually there is no comparison between MySQL as a real commercial heavy duty database, and MS Access which is typically a local use, giveaway in Microsoft Office. It is no good for remote access, its' connection system is not solid. It is generally useless for multiple user purposes.And you are far better using a web based interface for mysql, VB is also limited in functions and power. Consider using one of the free distributions of the Apache Web server which carries php as the scripting language, and the mysql database pre-configured. 


Go ahead with MySQL and experience it.