The idea behind using Access DB is,
a) you have MSAcces as a powerful tool to plan and construct your actual database
b) VB6 has powerful and 100% compatible object libraries (ADO) to work with an MDB (Access database file)

Propably the SQL EXPRESS David mentioned is also fully compatible with ADO (I suppose so), but I'm not sure what construction tools you have there. Access for instance allows quick and instant changes of table structures, adding a field here and there, helps formulating queries and might even directly import Excel data.