Looking for a cheap gaming projector

Under $1000, any recs? I don’t mind if the projection is small as I just need it to make a decent sided image (70-120) from about 10 feet away. If it matters, this setup would be in my room.

I'm considering the Optoma HD142x / 143x or BenQ or similar projector. I found this website very helpful because I have got a great knowledge about projectors.

Does anyone have any recommendations on these or similarly projectors?

Thanks