You might need to tell us what type of room you are in, size and if it's a batcave, or if there could be light coming into the room?
You have been given good suggestions. You say you want high def. and say 720p would be fine, but I imagine 1080p would work too, if at right price.
Your budget is around 650 dollars.
Doesn't sound like you need 3d, you never mentioned it.
Yeah, you need low lag as you are aware.
Now, I got a question for you, are you gonna be gaming next year too, because the NEW consoles will being coming out pretty soon, and they will be in 1080p.
Some of us got the viewsonic pro8200, because it is cheapest 1080p PJ, that has low lag for gaming. It is regular throw PJ, not short throw. It's is bright, sharp, long bulb life, 3 year warranty, has internal speakers 20watts (10x2). Now it could be in your price range of 650, if it goes on sale. I picked up mine 9 months ago NEW for 659 from newegg. When not on sale it's 799. Over the last couple of months it's been on sale to around 700 dollars a few times.
If you get optoma think about getting square trades or best buy extended warranty because it only has 1 year warranty/90 days on bulb, and a number of people in amazon reviews seem to say after 1 year things things went wrong with the PJ, white spots, and other issues.. Not everybody complained, but enough to concern me, but with extended warranty, you would be covered. If you get the pro8200 it does have 3 year warranty, so you don't need the extended warranty. Best Buy extended warranty for 4 years is 199 dollars.
I do like playing battlefield 3 on the pro8200, with 100 inch screen. I can make out detail that is hard to see on 42inch hdtv.
Once you are willing to spend over 1,000 dollars that would open you to other 1080p PJ's. I only mentioned the viewsonic pro8200, because it's the cheapest 1080p, that also is good for gaming, and watching other stuff, that got good pro reviews and user reviews. The 720p PJ's that were listed would be the best of the 720p PJ's.
Have fun researching.