Driver support, which was mature under XP because of its longevity, took a hit when Microsoft released new models for Vista and was late in delivering its DDK. On the other hand, driver support in Windows 7 and up have been pretty mature. In the case of Windows 8 to 8.1, my employer was able to get away with little to minimal updates of our software, which uses filter drivers, for compatibility with the new version of the operating system. The level of compatibility had previously been rare in Windows for us.
As far as hardware goes, the difference between specifications for Windows Vista, 7, 8 and 8.1 has been pretty small. A 1 GHz CPU, 1GB RAM and some disk space were the basic minimum requirements for each, if memory serves. Don't expect it to run great on that kind of systems for all uses, though, but it will run.
And, yes, a new version of Windows usually means new features, both in terms of hardware and software. So, it's not a bad idea to try and time your hardware upgrade cycles to coincide with Windows releases if you want the latest shiny bits, which, as you noted, third-party devs are developing for.