I've just been through a similar process as my 11 year old machine blew its power supply and it was going to be £150+ to fix.
LCD is the most common and is a bit cheaper. The problem with them is that individual LCDs can fail giving black speckles. A plasma doesn't do this, either the whole thing works or it dont.
LCD are better for fast moving action (football, motor racing) and for computer gaming. 100Hz machines are better still. 200Hz ? - only if you can see a difference.
1080p only comes into its own for Blu-ray videos. The current HD broadcasts (Sky and Cable) don't have enough bandwidth to display 1080p, they're more 720p. BUT technology will advance.
Contrast ratio (ie sharpness) is one of the more important things. The higher the better. When I bought my set 50,000 was the highest available. But now I believe 80,000 or even 100,000 are available.
For brands, I was told LG and Samsung are good mid market makes. The old traditional names - Toshiba, Hitachi are OK, but are slightly lacking. Sony is always good, but then you pay for it.
Prices have risen sharply within the last two months as the effect of the lower pound has worked its way through. (Contract/ item prices are agreed a good 6 months in advance)
The machine I bought was a 42LG5010 - 42" LCD, 1080p, with a contrast ratio of 15,000 for £549 in late April.
I think its a good machine and definitely superior to my old 29" tube. No problems with it yet, and I hope it will last a good few years. (my 11 year old 29" PHILIPS cost me £900, and served me well)