As to LCD vs. DLP, I wish I could answer that question. I have recently started looking at projectors myself as a viable option, they can be much more affordable for $$$/inch of screen size.
I know that one of DLP's problems can be what is known as the "rainbow" effect. If you are not aware of how DLP works, there is a color wheel that has the three primary colors on it (sometimes more) including a clear section for greyscale that spins in front of a DMD chip, which is what generates the images and has the lamp behind it. If the frame rate is supposed to be 60 Hz, then the wheel spins at 4 times that speed (note: some wheels have more colors and may be rbgrbg etc... in which it will have to spin faster). So... for every "refresh" or cycle, the projector splashes a green image, a red image, a blue image, and then the fourth for the grayscale at different times (it does this too quickly for our brains to decipher so we perceive an image in which all of the colors have been combined). Thus, at any given point in time there is an image on the screen with only one color, this can cause the illusion of a rainbow on the screen for some people, but not all. The "three chip" projectors that you have heard of try to alleviate this by having a separate DMD chip for each primary color, a prism is generally used to split the light from the lamp, the three primary colors then go through the three separate chips, and is then recombined before going through the lens, thus all of the colors are combined on the screen at the same time. With regard to image quality on one vs. three chips, they should be the same, its just with the three chips you are not going to have the rainbow effect. The disadvantage of having a three chip projector is the possibility of the prism going out of alignment when you change the lamp, which is something you can generally do yourself. I would just recommend wearing latex gloves while doing it so you don't get any oil from your skin on the lamp.
More info on DLP can be found at this Wiki, which I found to be most informative:
LCD supposedly doesn't have this problem, but I don't know what the advantages/disadvantages are of LCD.
I am personally going to start with a single chip DLP projector for cost reasons, I want to invest most of my money in the audio, and get a nice screen as well, then I can upgrade projectors later. Also, not everybody experiences these rainbows, so... if I don't then I luck out :-)
With regards to screens, they run the gamut, you can essentially spend as little or as much as you like. In my research I have found that Carada makes some excellent screens that are very reasonably priced. In terms of build quality and features, they are great for the money, which is what an internet shopper like myself looks for. All of their screens have a black border to absorb any light that may extend past the boundary of the screens, also they have screens with different gain levels, which is cool. Before doing projector research, I didn't even realize that a screen could boost or reduce the gain of the image from a projector!!! Their top line of fixed screens are at an awesome price point, for a 100" diagonal you are looking at around $581.87 if you want a smaller screen the price goes down from their, and up it goes up (duh).
In terms of calibrating the projector, I am not a pro, but I am a DIY kind of guy, and have a hard time paying someone to change my oil, let alone set up my home theater system. What matters to me is that the system looks and sounds good to ME, and besides, I look at this as a hobby, and want to do it myself. If the projector has sufficient menu settings to adjust color setting etc (something to consider when looking at different models)... then you can do it yourself. However, if you have the money, you can pay someone to do it. You may want to contact your local high end A/V store if you are interested in having them come out, as I have no idea what something like this would cost.
Hope I was of help, and look forward to seeing what other people have to say on the subject.