There are so many languages which are worth learning so giving advices is difficult. You know what? You need to learn one or two to get good experience and learn something new time to time, not doing too serious development, just for general culture and getting a change to switch to something better.
First of all, here is the most important problem: unlearn Basic. Seriously, this is the most difficult part.
I would highly support the idea of learning C#. F# would be very useful, as a door to functional languages. Python is very good to know. Many things depend on your interest to Web development; you may or may not need it. Most likely, you will need JavaScript/ECMAScript, just because this is the only thing on client side of the Web (VB script is not compatible with all platforms, don't get sunk into it.)
Now, how about VB.NET? It is a fully-functional languages, has most of the C# features (but not all of them). Here is the thing. Look at ECMA standards:
http://www.ecma-international.org/publications/standards/Stnindex.htm[
^]. C++/CLI, CLI itself, C# and Eiffel (also very useful to know). C# is also standardized with ISO. VB.NET will never be there. Also, there is a big social factor: if you need .NET help, you will find the most in C#, much less in VB.NET. Honestly, many developers won't just take VB.NET developers seriously. Just a fact of life. VB.NET developers feel offended and some might down-vote this post :-).
Good luck,
—SA