Tough question. This book is just a quick introduction for beginners so there are lots of topics that it doesn't cover in depth and others that it doesn't cover at all. If you want a better understanding of C# programming in general, look for a "Professional" series book or one of the others at that level. (My book "Visual Basic 2012 Programmer's Reference" is at that level for Visual Basic but I haven't written one for C#.)
If you know that you want to go into ASP.NET, then you could look at a "Professional" level book about that. Similarly if there's some other topic you want look into further.
There are also some more advanced topics that are generally useful and that are covered in their own books. For example, database programming, database design (see my book "Beginning Database Design Solutions"), algorithms, graphics, XML, Metro/Silverlight/WPF, etc.
In your case, it sounds like you've probably picked the two best approaches for you. I think if I were you I'd go with a general C# book first and then move towards ASP.NET if you still want to do that. (But I don't think looking at ASP.NET first will hurt you so I think you're okay either way.)