For some reason I thought Win 7 was for the touchscreens and MS had opened up Win 8 or 8.1 to offer both touchscreen and old-fashioned options. Am I wrong?
It's the other way around. Windows 7 has an upgraded but still traditional interface (essentially resemble Vista but with more features and significantly more performances and a more flexible UAC). There is an optional component for addressing touch screens but it's not enabled by default.
Windows 8 was designed primarily for touch screens. You can use it with a combo mouse+keyboard but it feels awkward (at least it does for me). Windows 8.1 is an attempt from Microsoft at gaining back the favors of those that use mouse+keyboard. Essentially Windows 8 is designed for touch screens, communications, social networking and such with tiles that can be easily manipulated with a finger even on small cellphone screens. There is some sort of "desktop" but it has been stripped of all the interesting functions present in Win 7. The latest figures are that Windows (all versions) power about 92% of the computers across the world; Windows 8 and 8.1 power about 13-14% (as of July 2014). Indeed the number of computers on which Windows 8 is installed has even lowered since the initial release (a lot of people went back to Windows 7).
Windows 9 (at least the preview we have) abandon the Windows 8 metro concept. Apparently Metro will still be present but as a "feature" integrated into a more classic desktop (which ironically enough has the same color scheme as Windows XP)...
Despite that I wouldn't describe Windows 8 as a bad OS -- once again it's perfectly fine... on my cellphone. It's just that MS took a step too far believing that suddenly all the users only had touch-screens at their disposal while touch screens still represent a very small fraction of desktop or even laptop computers (even if it represents most cellphones). Indeed MS seemed to believe that Mass Effect was the present

Say, in 10 years maybe that will be the time for Win 8... but not now.
Regardless, these prices are only for downloads. Can you download Windows, or does it require a disk?
You don't need a disk if you perform an upgrade from a previous version of Windows (the components of the new version are downloaded via MS site and installed automatically). You still need a DVD or a bootable USB key in case of a new install.