When I started, my first language was VB6 (regrettably; I should've started with VB.NET) and there were several things I wanted to do in code, but couldn't. VB.NET, in my opinion, is more complete because its Object-Oriented, which is the language that makes the money. In my personal opinion, VB.NET does everything VB6 couldn't/can't. For those IT Professionals to-be or those that want to have command of a language that has functionality way beyond the bounds of VB6, turn to VB.NET.
If you're just wanting to learn how to code because you heard about it and think its kewl, start with a language that will actually DO something for you in the future. VB6 is hardly used in businesses because people find it more efficient to program with an Object-Oriented mentality.
There's my 2cents...