For Windows, you may want to check out lcc win32 and Pelles C, these are both very lightweight and freely available C IDEs, that also provide an integrated debugger, online help and other useful features.
The downloads are both less than 10 MB and it's easy to install/uninstall both of them. Also, they run both fine under WINE on Linux.
In my opinion, having a lightweight learning environment is essential when learning a new language, otherwise you are likely to possibly mostly learn to work within a certain environment (IDE), rather than learning the fundamentals first.
In other words, just installing, configuring and using huge IDEs such as Eclipse or MSVC++ Express can be daunting task for a newcomer, especially because both of these IDEs are so powerful. So, I would recommend to concentrate on getting familiar with compact tools and platform-agnostic stuff. Personally, I would hate to install several hundred MB of software tools, just to learn C.
A lightweight compiler such as lcc-win32, pelles or even tcc is a much better tool in my opinion.
Of course, eclipse can be very useful if you may need to also work on other platforms, because then, you can work with one environment on pretty much all platforms.
Also, if you do know that you'll mostly work with the MSVC++ IDE in the future, then using just that also for learning C is probably not a bad idea either, especially because you may already be familiar with some of its concept from working with C#.
However, note that learning C is not about learning how to work with MS Visual Studio, if you only ever know how to program in MSVS, you'll not be a very capable in general, simply because you are restricted to one specific platform and even working environment.
When learning how to drive a car, you are also not restricting yourself to one make and model, but instead generally learn how to drive most cars that follow standards and conventions.
If you were to restrict yourself to just one specific platform and environment, you would also reduce your employability, no matter if you're a driver or a programmer.