Plasma TVs used to dominate over LCD because they were bigger and had a better picture. LCDs have caught up a lot and the two technologies are in a good old fashioned market driven fight. LED HDTVs are a new breed but very expensive. In the near future LED TVs will be as thin as a credit card and will go on a wall like wall paper. The technology is very new and expensive. I wouldn't suggest getting an LED just yet. Choose between a Plasma or LCD screen for now and wait until the price drops and the technology of LED HDTV evolves.
Plasma wins out in the contrast ratio category. This is the difference between the darkest darks and the whitest whites. The contrast ratio of LCD screens has caught up but still can't beat Plasma.
If you are going to be using your TV to view still images or as a second computer monitor (which is fantastic with a Mac Mini by the way), LCD wins out. our flat screen computer monitors are LCD technology because they handle still images the best.
For moving images, like chase scenes in movies, Plasma wins out. LCDs have caught up a lot but there is still a lag time that Plasma definitely has an edge over. Plasma TVs can be viewed from almost the complete side. If your room you'll be putting the TV in is small though, this shouldn't really matter.
Both Plasma and LCD have similar lifetimes, the biggest factor depends on the manufacturer. This is why you should get HDTV ratings for whatever set you are looking to buy. Don't base your judgement on number alone, because they can be made up by the manufacturer. TV companies say "1,000,000 to 1 contrast ratio", which is a total lie. So, make sure you read online reviews of the TVs and also view them in person at a Local TV store or a Best Buy.
For very large HDTVs, like 50 inches and bigger, Plasma TVs have shown to be more resilient. This has to do with complicated electronics theory. Just note that if you are planning on buying a big set, Plasma is probably superior. Samsung and LG have made very large Plasmas that have proven to be very good.
When it comes to power consumption, LCD are still best, which is another reason they are used in computer monitors. This is simply because the neon gas that is inside a plasma TV takes more electricity to light up. The LCD TVs use about half the power generally.
You get what you pay for. A $4,000 TV will definitely be better than a $1,500 model but the enhancements aren't necessary for your average TV watcher. When in the store, take a look at the picture on the different models. Real TV buffs are the only ones who will find the picture quality difference enough to spend the extra money.