A solid 1080p projector will set you back around 400$ new, even less used - that’s for a reputable brand. I’d say they’re cheap to the point where bothering with potential Chinese crap isn’t really worth it… And these can do 100" from a distance of about 2m - that’s for long throw models. Short throw projectors can do the same image from right next to the screen, basically - depending on how you plan your setup there are options.

If you’re just getting into the topic you might want to read up on DLP vs 3LCD as well.