things to consider when choosing a projector:
1. noise level of projector (bothers some people, others not so much). really noisy ones bug me personally. look for noise db rating.
2. brightness (measured in Lumens). if you have low lumens, it means you may be limited to playing in a darkened room in order to see the picture. if high lumens, u can see the projection quite well even in the daytime/open curtains
3. contrast ratio - this determines the range you get between darkest and lightest parts of your image. higher the better!
4. image size/throw distance - this relates to how big you can display the image, how close your projector needs to be to the wall and how long things stay in focus the bigger the picture/further away the projector is etc
just check specs of different projectors in your price range and then go for it
