The least expensive option is LCD, and probably the way to go to get the best "bang for the buck". Look for at least two HDMI inputs, three or more if you plan to use an Xbox, Wii or PlayStation. If you plan to get a Blu-Ray player, go for 1080p resolution. If all you are going to do is watch cable, over-the-air broadcasts or standard DVD's, 720p will suffice, unless you're planning to get a 50+ inch model. If so, then get the 1080p.
While LCD sets use fluorescent tubes to provide the backlighting for the screen, LED sets use arrays of Light Emitting Diodes and are generally thinner and run cooler. The LED arrays will have a longer life than the fluorescent tubes, but either one will probably last long enough until you replace the TV. The newer sets are LED, and are usually accompanied with other features, such as the built-in capability to display internet content without using a computer attached to the set.
I'm not familiar with "Quartz", and googling doesn't return much, either.