Best for Gaming

Top pick
Samsung - The Premiere LSP7TRunning these analyses costs money. Buy through my links to help keep lights on! I may get a small commission.
A good quality 1080 projector that can pass through 4K content is fantastic (especially on a 100 inch). I have a 1080 BenQ and haven't felt the need to upgrade to 4k yet. I get the mastering and bitrate of 4K discs, just not the actual raw resolution. I didn't have to spend over $1000, not even close. In fact I spent $425, which is *insane* for the level of quality. It works out very well. Though I may have to change the bulb soon lol.
It's good. Many of us have been down your road, till we understand that there's always better projectors that can fit a budget. I had a 720, moved up to be BenQ 1080p, and an Epson 1080p. I'm thrilled with these two and one day, when I get some cash, I'll try a 4K. But you're doing good. And they won't be as loud.
Projectors last a long time, so spend the money on a good one now. I picked up a $750 1080p Benq, expecting to replace it within three years. It's been eight. I'm now willing to drop $5000 on an Epson LS12000 because I now know it will last me a decade. Silver Ticket screens are solid. Sure the Steward is better, but there's diminishing returns after a certain price. You can always upgrade your screen at a later date, but I doubt you'll feel the need.
Have a look at Richer Sounds. I picked up a BenQ 1080p projector for £200 and gor a discount for signing up to their newsletter. It was a return / open box. I was projecting almost my full wall height - it was amazing. Room layout change means a smaller projected size now but still great.
End of reviews
Top recommendations from others in the same boat

Top pick
Samsung - The Premiere LSP7T
Top pick
Samsung - The Premiere LSP7T