Here are my thoughts.
Definately go 1080P if you're getting a TV larger then 40", below that, don't bother (and some under a certain size are not even available in 1080P).
There are four common Hz's out there, 60, 120, 240 and 600. The first three are really relevant to LCD, the last is for Plasma (but it doesn't really mean the same thing). Hz is refresh rate, how fast the image refreshes, the faster refresh the smoother the picture (ms is also important, but hold that thought). When LCDs first came out there were two major complaints, poor image refresh resulting in juddering images and poor black contrast. The first has been somewhat mitigated by the increasing Hz (screen refresh rate) and also the increase in pixel response time (ms). For Plasma, refresh was never an issue due to the technology difference, so until recently, Plasma didn't offer a Hz refresh, but started recently as a comparison (there is some math behind it, but for intensive purposes it means little).
Pixel response time is very important with LCDs as this helps determine the smoothness of the image as well. The faster the response time (lower the number) the smoother the picture (relevant to refresh). A good LCD should perform around 2 - 4 MS, anything higher is going to start to be noticeable.
Black level is another major flaw of LCDs, they cannot produce the same black level of Plasma, it's all about technology differences. Things have improved with new technology, but they're still not flawless and don't produce as deep of blacks.
Now onto Plasma, it carries two major complaints, power consumption and burn in. The first has changed dramatically in the past few years. Three or four years ago, you'd see power usage around 400W (about the same as a home computer), now, for most they are closer to about 200 - 250W. A comparable size LCD will probably close to a 100W.
Plasma burn is probably brings back memories of the old projection screens which had this same issue. This issue is probably a little more played up then it needs to be as most screens either have image shift technology to prevent it, or will auto correct in a few hours of watching something other then the image that was retained. Retention is not permanent and most times its only noticeable (if a temporary image is retained) on really white or black scenes, it will not be noticeable during normal watching.
So what does this all mean, well you need to determine what you match most. If you watch a lot of sports and movies in artificially lit rooms, I'd go Plasma. It will offer the most fluid picture, no image lag and blacks/colors that are very true. If you watch more regular TV in a brightly lit room (think outdoor light), you're probably better off with a LCD screen.
The newest TV to hit the market is the LED, but really its just a LCD with a different backlight component. This helps with producing better blacks (the individual LEDs can react with the image versus a fixed backlight), but it doesn't fix any other issues. There are also Ultrathin Plasmas (if you want the cool 1" factor), they still suffer the same issues as a normal Plasma, but again, just really thin.
Some other considerations are cables/signal, you should definately use a HD box and HD cables, with the preference to HDMI. DO NOT BUY an HDMI cable from BestBuy,
Walmart, etc, they are extremely overpriced for what you get, look online for the cables, places like monoprice.com are a great place to start. To give you an example, I just bought 8 - 6' HDMI cables for $20.71 shipped, try doing that in a retail store, you'd be spending close to $150 - $200 for the same.
Finally for me, Plasma works the best for my needs, I watch a lot of movies, the room it is in is mostly artificially lit and it offers a superior picture for my needs. I am on my 2nd Plasma and the only reason a bought a new one was my old one was only 42" and 720P, the new one is 50" and 1080P.
I'm thinking I need around 46"-50"?
