Below is a list of projectors that will work great for this kind of project. Click on the titles to purchase from Amazon. Amazon has pretty good pricing and they often have used products available that can save you some money. It isn’t possible to list all of the projectors that will work so you may want to Browse Amazon For Short Throw Projectors
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If you are on a tight budget, you might also check out the auction sites like eBay for good deals on used projectors. For specific info about the type of projector you should be looking for, check out this page.
Optoma GT1080HDR Short Throw Gaming Projector | Enhanced Gaming Mode for 1080P 120Hz Gaming at 8.4ms | 4K UHD Support | Play HDR for 4K and 1080P | High 3800 lumens for Day & Night Gaming, White 1080p (1920 x 1080) resolution and 3800 lumens. Short throw so you don’t have to move it back too far to cover your house. About $800.
Optoma EH412ST Short Throw 1080P HDR Professional Projector Short Throw, 4000 lumens bright and 1080p (1920 x 1080 pixels) resolution. Accepts 4K input if you want to use it for other purposes. About $1,000.