Being someone who has a HTPC and uses an LCD TV as the monitor on that system, let me give you some help.
Not all 1080p LCD TV's will accept a 1080p signal. You need to read the fine print here and look at what the inputs accept. Many will only accept a 720p or 1080i signal and upconvert it to 1080p. A true 1080p TV will be 1920x1080 resolution. Now, you will have to watch out for a lot of things.
LCD TV's usually have a lot high input lag as well as motion blurring compared to what you will see in the 30" LCD monitor range (since there is no such thing as a budget 30" LCD monitor, they are almost all top of the line with the latest technology and best panels. A budget 37" LCD TV will have a much worse image quality than a 30" monitor. The color space of almost all LCD TV's are horrendous compared to a monitor. However, a high end LCD TV can be on par. That said, you don't see very many high end 37" LCD TV's because the high end usually stops at 40". If you go for the LCD TV, I would recommend looking at the Samsung 81F series. This uses LED backlight, which allows a much finer tuned gray-scale because it dims the individual LED's behind portions of the screen which are dark, and brightens the ones behinds areas that are bright. Traditional CCFL backlight can not do this, as it is either on for the entire screen or off. The LED's also produce a specific wave-length of light, which means the manufacturer's can do the math and get exact color outputs from the LCD crystals. Again, with CCFL backlight, it produces multiple wave-lengths of light, all of which will have their own slightly different color, which means when it passes threw the LCD crystal, slightly different colors will output, as well as the inability to generate other colors where were not part of the incoming light's color spectrum (since all the LCD crystal does is filter out colors except the green wavelength component for the green sub-pixel, the red wavelength component for the red sub-pixel, and the blue wavelength component for the blue sub-pixel). If the light that is being filtered thru the liquid crystal does not have equal parts of blue, red, and green wavelengths, the display will be shifted towards one or more of those colors, and as a result will not be able to produce certain combinations of color output, and its color space will be limited.
I use a 46" Sharp D92 series, which was their top of the line model when I purchased. You really need to look at the top of the line LCD TV's if you hope to even compare against a monitor.