1) Don't convert for the sake of converting. IF it works, leave it alone.
2) Having said that, if you want to make changes, your best bet would be VB.NET (and you can get the Express edition for free from MS)
3) DO NOT CONVERT. Let me repeat that DO NOT CONVERT. Re-write the application. You'll still be able to recycle some of the code, but for what it's worth, do not use the converter to upgrade your VB6 app to .NET. It does a hack job at that, and in some cases, doesn't event do a convert, but just wraps things up.
4) You'll want to learn how to use ADO.NET ... which is a different paradigm from previous database models. There's an FAQ/Tutorial in our Database section that gives a pretty good overview.

-tg