new projector for a new projector-user

Hello all,
I'm sure this question has been asked a million times, but since I really am new to the Projecting area, I'd like to ask what a good choice would be for me to buy. I will lay out my intended uses and my current equipment, as well as my goals and where I'd like to see this system go. My budget for a projector is $1500 or less, including DIY installation, screen and cabling.

I currently have a 480P DVD player (Panasonic), a dish network DVR box (standard-def) and an Xbox (the original). Right now everything hooks up to a Mitsubishi 65" RPTV that supports 480i, 480P, and 1080i. It makes a beautiful picture in HD (it has a built-in HD tuner) and handles lower-res sources well. I would like to convert my existing setup to a projector that supports a minimum of 480i, 480P and 720P. Getting 1080P is probably out of the question at my price point, but 1080i would be nice (I'm not even sure projectors do 1080i but I would assume they do). I do not have a preference between DLP or LCD models, or between particular brands, although some of you I'm sure do, and I hope you'll take the time to explain why a particular technology would be best for me. I do not currently have any HDMI sources, so I need a projector with Y/Pb/Pr inputs. I can do component switching with my receiver (Denon AVR-1803) if necessary. I would be adding a PS3 or X360 to this system in conjunction with the projector, so please figure that in to your suggestions. The X360 is my current favorite, primarily because it has component outs (I do not know if the PS3 has component outs).

If there is anything else I should add please write and let me know. Thank you all in advance for helping me pick the right model, and yes, I do love parenthesis (by the way, my wife wasn't COMPLETELY against this idea, so I'm kinda psyched!)