Actually it's a great thing to have to make a choice between these two competing TV screen technologies. You really can't lose either way that you go, because both LCD screens and plasma TV screens produce a much better TV image than anything that has been available in the past. But there are some differences that you need to know about to make the best decision for your own use.
Both LCD and plasma TVs can be very thin in configuration and produce a flat panel picture that is similar to watching a movie screen. Plasma TVs though can be a little thinner than LCDs, so if space is a major consideration you may prefer the plasma screen for that reason.
The major difference when viewing both screens is that the plasma screen does reproduce more solid black than LCDs do and so it has a more contrasty picture. For some, this is a good thing, for others it doesn't really seem to be an issue. So before buying be sure to make your own comparison and decide for yourself which screen fits you best.
One other difference is that plasma TVs run more hot than LCD because of the technology used to display the screen colors. So a fan is usually used in a plasma TV monitor to help cool the unit while it's running. Depending on the manufacturer the fan can be easily heard while it is running, so if you have settled on a plasma TV, be sure that you check out the model that interests you and listen for fan noise before buying it, getting it home, and then deciding that you can't live with it.
Another small difference is that plasma screens have a reputation for being susceptible to screen burn-in, where an image that has been on-screen for some time is still faintly visible even when viewing a different program. Actually the bad rap that plasma TVs have gotten on this matter is mostly overrated and is usually only a problem when an image stays on-screen for an extended period such as a video game that is paused for a long time and left on the screen. LCDs don't suffer from this problem at all though, so just decide whether your viewing habits could possibly introduce a burn-in problem or not beforehand, and make your decision accordingly.
As was stated above, either kind of monitor will most likely suit you well as both technologies are fairly mature and well-developed. But being aware of the subtle differences will always lead to making a better, more informed decision.