In all cases, whatever platform you decide on, first learn the language. That will provide a base from which you can build on. Then you can learn the associated frameworks for whatever medium you want to reach people through your software.
As far as c# goes... once you learn the language, you can expand your knowledge to things like:
- ASP.NET for the web
- Silverlight for the web/desktop/mobile
- WPF for the desktop
- XNA for desktop/mobile/console
And that's a small focus on some of the options for presentation; there's more. Then you have backend, middleware, etc. There certainly is a lot to it, and it probably seems daunting now, but it all starts at the language.
This is consistent with other large languages/frameworks. They're not all made equal, and your preferences (once you know what they are) will dictate which you enjoy more.
From my completely subjective point of view as a c# developer: I say go for it. There's lots of doors to walk through and windows to fly out of once you've got the language under your belt. And the language is only getting better with age. Who knows, web development looks cool to you now, but maybe you'll fall in love with something totally different.