If you could up your funds to $549 and live in a state with no tax on Amazon, you could get the Epson HC2000 (sale ends 3/29). Two year warranty, bright, filter (to keep bugs out), replacement lamps only cost $99, 6000ish hour lamp on eco, built in lens cover and it is 1080p for $549.
Well it depends on how much light you have around the screen. What is your throw distance (distance of the projector to the screen)? Will you be using it for front projection or rear? What size screen? How far back will you sit?
I assume you want something you can take out for night time viewing and probably want a large 16:9 screen say 120 inches or 144 inches. You will need sound because the built in projector speakers don't cut it.
Measure the distance from where you want the screen to where you want the projector. That will be your throw distance. Make sure you do the throw distance calculator to determine if the projector will work for the size screen you want since you lose placement flexibility with the cheaper projectors.
For example, take your distance of 20 feet. If you put the Epson HC2000 at 20 feet, you will have a 16:9 image of 185 to 223 inches. Just search Epson throw distance calculator and plug in the distance. This might not be the projector for you at 20 feet unless you want to go really big and do a 200 inch screen.
You could spend more for a more for a better projector or look at the 720p projectors and play with distance calculators. Or you could try a different spot for the screen and projector. Maybe a short throw projector or do a rear projection screen. My 92 inch screen can be either and it comes in larger sizes.
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