Wow, what an array of answers and all of them have some right and some wrong in it. Here is some of the real stuff.
First of all, if you learn VB 6.0 it does help you learn VB.NET. That is because they are both VB and so the syntax in one is very similiar in the other. Does that mean you should waste your time with 6.0? No not really. A beginner can jump right into VB.NET and learn that fine without 6.0. It might even be a waste of your time to learn 6.0 these days, because like one person pointed out, 6.0 is quite a bit obsolete.
Second, VB.Net is generally better for beginners than such languages as C# which are rooted in the foundations of C/C++/Visual C++. VB.net is generally more word oriented (reading its code is more like reading a book) than C# is. Again, not saying that someone can't jump straight into C# because they can like all the other languages of .NET.
Third, learning any .NET language gets your foot in the door to any other .NET language. Microsoft is in the process of merging the different languages together into one common platform with its own syntax... (the Common Language Runtime or known as the CLR).
I recommend you go VB.NET first because it is what the industry is doing now a days. VB 6.0 is only in a few companies anymore maintaining old legacy systems. Once you learn VB.NET, you can easily jump to C#, VC++.NET, ASP.NET etc.
However, if you need or want to, you can also step down to VB 6.0 and pick up fairly quickly once you learn VB.NET because the syntax is very similiar, the concepts are just a little different.
Take it from someone who has had formal training in VB.NET, VB 6.0, C/C++/VC++ and many other .net languages.
I hope this clarifies some things for you. Enjoy!