In that case, it depends on the job. If you'll need to work with old ASP applications, then you'll either need to learn VBScript, Javascript, or both. But if you want to be able to do new development with .Net, there's no point in spending time on VB6 or VBScript.
As far as where to start, it really doesn't matter. If you are interested in web development, I'd just start with a good ASP.Net book. That way you'll be learning about the .Net environment, web forms in general, and the VB.Net or C# language, all at the same time. At the same time, learning database development will also be crucial in the vast majority of development jobs.