As far as which language you should learn, well what are your experiences thus far? I prefer C# over VB.NET. Though, eventually, you should be able to program in VB.NET even if you say with C# as your primary language (the same is true vice versa for VB.NET). You might want to check the syntax of each language and see which you prefer just by first glance. You will probably find that whenever code examples are provided for .NET and both languages aren't present, typically the examples are in C#. This is not a big deal though. I find C# (and similar languages) to be less verbose but that is a preference. Here are some good resources. I highly recommend the LearnVisualStudio.NET videos; start with the beginner tutorials and advance to more advanced topics.
Some great resources include:
http://www.dotnetrocks.com (podcast)
http://www.se-radio.net (general software engineering podcast)
http://www.haacked.com (Phil Haack's blog)
http://weblogs.asp.net/scottgu/ (Scott Guthrie's blog)
http://stackoverflow.com/questions/551315/which-c-net-blogs-do-you-read (previous question with a good list of blogs)
http://www.learnvisualstudio.net (good place to find video courses, cheap)
http://stackoverflow.com/questions/54423/best-net-podcasts (previous question)
http://stackoverflow.com/questions/1644/what-good-technology-podcasts-are-out-there (more podcasts)
Open Source projects:
http://www.codeplex.com is great for Open Source .NET projects.
Also:
http://csharp-source.net/ (not bad, some projects are old and not maintained)
http://sourceforge.net/softwaremap/trove%5Flist.php?form%5Fcat=271 C# as SourceForge
http://stackoverflow.com/questions/13765/open-source-c-opportunities (previous question with good infor)