Right - this was my career before being made redundant.
Plasma Flat panel displays were intially designed for static images and early models had great trouble displaying complex moving images like TV.
After a while they were used in high end home-cinema for a few years along with projectors and big quality CRT stuff.
LCDs were very expensive to make and performance was very poor from early displays.
A few years of jiggery pokery later, China has basically made flat panel LCD displays cheaper for all.
Then the fashion police came along and said flat panels are the in thing - so out went the 80 year old CRT design, in came the sparkly flat LCDs.
Plasma TVs still have a much higher contrast ratio than the current generation of LCD displays. This means that they are better at everyday stuff in a bright sitting room (however, all that glass makes a plasma VERY heavy and not so easy to install in the average home. LCD panels can be much lighter).
When buying your first flat screen, look for brightness and contrast information in the features list, a bit like:
Acoustic Solutions 42IN HD Ready Digital Plasma TV.
Resolution: 1024 x 768 Pixels.
Contrast Ratio: 10,000:1
Acoustic Solutions 42in HD Ready LCD Freeview TV
Resolution 1366 x 768 pixels.
Brightness 500 cd/m2.
Contrast ratio 1000:1.
Viewing angle 178/178 degrees.
Taking the two examples above, the plasma is capable of much brighter pictures but not capable of displaying high resolution sources such as 1080i HD.
The LCD can display high res stuff but not very well....
Both types of display can suffer from 'video latency' - this is where a screen can simply fail to keep pace with the information on the screen - football is perfect to demonstrate this as the ball disapears into a pixelly mess somewhere on the pitch - the better defintion the ball, the better the quality of display.
Confused? Damn right!
Quantity over quality -
big LCDs can be cheap but performance can be poor when displaying complex information.
Plasmas are almost as cheap but can be limited in resolution and performance can be poor.
Go to your favourite electrical store: ignore brand names (meaningless these days!) and simply stand back and look at what YOU think is the best picture for you.