There are so many ways to save data, that we can;t rellay recommend anythign without knowing a heck of a lot more about your application:
Text files,
Binary files,
CSV files,
Excel,
Access,
SQL databases,
MySql databses,
SqLite,
SQLCE,
...
Just to name a few!
But...your use of the word "database" raises a few flags: I would suggest that you really need to start reading up on using databases before you go any further, because there are a lot of potential mistakes you could make, and you need to learn the basics before you start doing anything serious.