I run SHIII on Windows 8.1 and it's rock solid. The only fix I needed was setting SH3.exe to run in compatibility mode with Windows XP Service Pack 3.
Also, I've run the game in several forms of fullscreen. 4:3 with blackbars, or 16:9 with Conus' Widescreen mod for example. You need to configure your video card to correctly rescale the game to your liking, if needed.
I actually use
Windowed Borderless Gaming to run the game in a fullscreen windowed mode so I can mess around on my second monitor without minimizing the game.
In short, SHIII works great on 8.1. Couldn't be happier.