Mysql is the most pervasive, reliable yet cheap/free and open source. Despite having to buy a sql server, you could use mysql for your backend data storage RDBMS software.
To connect mysql from vbnet or other net related language, you could use odbc driver. Just download the odbc driver for your operating system (that is windows). from here.
Tags: connect mysql to vbnet, vbnet 2008, vbnet 2005, vb.net, programming