For sure you are looking for a free database so for that you can use many databases like mysql ,postgresql , and sql server msde or access
but we still have other scenario, if you are going to distribute this application to other pcs so you have to think about deployment and in this case you can eliminate the mysql , postgresql because they depend on servers but msde (it's also server ) is much easier and you can found alot of tutorials how to deploy it with your project
It depends on how much you are expert in database and for what reason you are using it? are you going to need complex queries or it just a storage place for the data ?
if it's complex query i will go for msde for sql server if it's only for saving information may be i will go for access or even xml