How do I decide whether to use ATL, MFC, Win32 or CLR for a new C++ project?
It depends on your needs.
Using the CLR will provide you with the most expressive set of libraries (the entire .NET framework), at the cost of restricting your executable to requiring the .NET framework to be installed at runtime, as well as limiting you to the Windows platform (however, all 4 listed technologies are windows only, so the platform limitation is probably the least troublesome).
However, CLR requires you to use the C++/CLI extensions to the C++ language, so you'll, in essense, need to learn some extra language features in order to use this. Doing so gives you many "extras," such as access to the .net libraries, full garbage collection, etc.
ATL & MFC are somewhat trickier to decide between. I'd refer you to MSDN's page for choosing in order to decide between them. The nice thing about ATL/MFC is that you don't need the .NET framework, only the VC/MFC runtimes to be installed for deployment.
Using Win32 directly provides the smallest executables, with the fewest dependencies, but is more work to write. You have the least amount of helper libraries, so you're writing more of the code.
Win32 is the raw, bare-metal way of doing it. It's tedious, difficult to use, and has a lot of small details you need to remember otherwise things will fail in relatively mysterious ways.
MFC builds upon Win32 to provide you an object-oriented way of building your application. It's not a replacement for Win32, but rather an enhancement - it does a lot of the hard work for you.
System.Windows.Forms (which is what I assume you meant by CLR) is completely different but has large similarities to MFC from its basic structure. It's by far the easiest to use but requires the .NET framework, which may or may not be a hindrance in your case.
My recommendation: If you need to avoid .NET, then use MFC, otherwise use .NET (in fact, in that case, I'd use C# as it's much easier to work with).
As far as C++ goes, I would use WTL. It's lightweght and you will have few (if any) dependencies, making it easy to ship and install. I find it very satisfying when my app consists of a single EXE that will run on most versions of Windows, but this may not be a concern to you.
If you choose to go .NET instead, then C# is almost certainly the way to go.
More in WTL here:
http://www.codeproject.com/KB/wtl/wtl4mfc1.aspx
I would be very curious as to why you would do this in C++ at all. Based on your brief description, C# sounds like a much more appropriate choice.
Just to elaborate a bit, look at the link you gave describing the C++ CLR. The top rated answer notes (accurately, in my opinion) that C++ is appropriate for "kernel, games, high-performance and server apps" - none of which seems to describe what you're doing.
MFC, ATL, etc are going to be supported in the sense that, yes you'll be able to compile your app on future versions of Visual Studio and run them on future versions of Windows. But they're not supported in the sense that there's not a lot of new development going on in the API or the language the same way there is in the CLR and C#.