Beginning ASP.NET using C# is an excellent book. With the coming of C#, i think you need not be too worried about VB.NET.
And don't get confused with .NET and ASP.NET, .NET is the whole infrastructure and ASP.NET is just part of it.
ASP.NET is the next generation of Active Server Pages. ASP.NET introduces a new paradigm to server-side Web development.
ASP.NET is a programming framework that enables the rapid development of web applications and services. Part of the emerging Microsoft .NET Platform, it provides the easiest and most scalable way to build, deploy and run distributed web applications that can target any browser or device.
Microsoft is in the process of building an entire new low-level infrastructure for Windows. This new infrastructure, when used, sits between the low-level Windows operations and user applications, managing the code execution. This infrastructure, labeled the .NET Common Language Runtime (or CLR for short), provides a level of encapsulation between the developer and the operating system, thereby making writing Windows programs simpler. No longer will the developer have to worry about low-level details such as memory management, pointer management, language differences, and other common annoyances.
ASP.NET is different from ASP in two major ways: first, ASP.NET offers several programmatic enhancements over ASP. Microsoft really did a great job of listening to ASP developers' comments and ideas for improvements and incorporated those improvements in ASP.NET; second, ASP.NET offers a change in programming fundamentals, in the way you write the code for creating these pages.