SQL Server Express will certainly do the job, but it does require that a server be installed. If you want to avoid that then you can use SQL Server CE or Access. SQL Server Express and CE are fully integrated into VS, while Access would require the Access application to be installed.

You can check out the Database FAQ link in my signature for some local ADO.NET resources. The MSDN Data Walkthroughs and How Do I Video links would also be useful.