For the apps I'm writing in Visual C#?
Well, the minimum requirements for your application written in C# is probably going to be the .Net framework, which has a nice page here listing the requirements for the various versions.
How usable will your app be using the recommended minimum? You'll have to find some hardware (or use a virtual machine see comments) and try it out.
It depends from the kind of application you are writing. For example a 3d videogame could require DirectX capable hardware. If you are writing an office app (wordprocessors and so on) every modern computer with .NET framework is enough :)
I would suggest setting up a VM with just your software installed and then just alter the ram and processor specs on it and retest.
It will take a little while but this would be a great way to do determine it and see what areas that you application could be enhanced.