DLP does not give better blacks or contrast ratios, they do offer sharper motion detail but the 1 chip models can suffer from the rainbow effect, also much depends on if you are prone to noticing that, a 20 feet distance from lens to screen offers you much flexibility and basically any model...
Forget the specs which say 50,000-1 contrast ratio etc etc, they are all worthless, bit like speaker watts, concentrate on what you need which is a good gaming projector with good black levels for movies, if you can stretch the budget to over $2000 you will find a few that may fit the bill such...