I've got an old ~2009 gaming PC that I use for a game called Stepmania, and while the game itself can be run on a potato, I'm mostly looking to build a system strong enough to screen record it at 1080p and not constantly drop down to 30-40 fps. It's a really old computer, the GPU is a GTX 460 and the CPU is some Intel quad core at 3.0 GHz. It has a modern SSD in it though.
What's the cheapest build I can do that will be able to screen record (OBS Studio) 1080p and not lag/stutter? I literally only use the computer for playing this one game, and have a separate "main" computer for normal use, so I can cheap out and cut corners for this one.