Simple database application for Windows
I would recommend Sqlite. It's completely self-contained, and public domain so there are no license issues at all.
Single user or multi user?
For single user, the answer would be SQLite
For multi user (or multithread), try MySQL or PostgreSQL.
Since your requirement is a windows based application i would suggest that you go with sql server 2005 express edition which is a free tool, but with certain small limitations. you can upgrade to a bigger version when you go with a paid version.
There are other DB engines like SQL Lite or FireBird, choose them if the support and growth options they provide are good enough for you
Additionally, Visual Basic is eof lifed. VB.NET might be a better windows based platform currently. It would give a better platform / features to start with and when you want to expand the talent you have working on the project, i assume .NET talent might be more available than programmers who want to work with a dead language.