TS12 works fine with Windows 8.1. The requirements are the same as they are for Windows 7. You will need to install and run the program as administrator.
The new start menu-thing is a bit odd, but with the desktop mode, things look just like Windows 7 except for the smooth window frames. The desktop is actually an application of sorts and can be resized when other Windows 8.x native applications are running. You can also quit the desktop, which I have done in error, and then go back into it where you left off without affecting the application that is running on the desktop. The start menu doesn't need a touch interface. You can scroll between applications by simply rolling the wheel on the mouse.
I spend 99% of my time in desktop mode since that's where my applications reside, as they are older Windows 7 era applications. For these applications, I have taken the multitude of desktop icons and placed them in a folder I call Desktop Apps. I can then run the application from there without cluttering my desktop with icons.
Stability wise, Windows 8.1 is very good. Windows 8 originally had trouble with my motherboard, but subsequent driver releases and now Windows 8.1 have proven to be very stable.
Once you get used to it, you'll find the operating system to be very powerful. There are lots of hidden gems in there that are not so obvious until you start working with it, and once you do stuff in Windows 8.1 and go back to Windows 7 you'll look for the missing features there and get confused.
John