The most important is your GPU. If you have a modern GPU you should be able to run stable diffusion locally. I've got an older GeForce 980 Ti, and I can run it it, but I did have to tweak the settings to lower the VRAM usage so that it didn't crash all the time. Still crashes sometimes with larger models and higher steps and such. I also have to limit my images to 512x512 to keep it within my VRAM budget, but I've been able to get larger images by upscaling.
I guess what I'm saying is that if you've got a better GPU than I do, you should get better results than I do.