360 sticks have native Windows support don't they? Kinda like the 360 pads?
Yes. Xbox 360 pads and sticks share the same Windows drivers, and are the default standard for PC games that require/need/lean on controllers. They'll work with any game that mentions or recommends full controller support. I think you need to be connected to the internet to download the drivers for the first time, but once you install them you're groovy anywhere.
PS3 stuff can be read as a joystick using generic driver, but some games don't like that and you need to download separate drivers that emulate 360 controller inputs. I know USF4 PC supports PS3 sticks without having to do any shenanigans, and other people can back me up on that.
PS4 sticks work similar to PS3 sticks, generic drivers, but I use my PS4 stick to play all my fighters without issue on PC. Even works with DoA5 (lol).
Xbox One sticks and pads have PC drivers now, but I've never tried or tested one on any fighters I've owned. Someone else will have to vouch for it, but I would be extremely surprised if it didn't work the same way as 360.
tl;dr if you game on PC and you own a PS3/360 stick already, you're set for pretty much the next decade. Unlikely that support for XInput would ever be shuttered.