That's going to make it easy
From what I reckon, you don't need a new TV just stay with your 20"!

Just kidding
Seriously, You obviously don't need the latest/highest/greatest thing out here. To give you an idea about specs and tech. available:
Full HD: 1080p, biggest resolution on the consumer market, and it's a must for Blu-Ray.
HD Ready *usually* means (it's a loose term): 720p - Although it's considered HD, it's nowhere nearly as crisp as 1080p. It's about twice as big (in term of resolution) as a regular TV.
Basically, the higher the resolution, the better the image. HOWEVER, for the same resolution, the bigger the TV the lesser the image quality (Imagine a 40" and 52" TV with the same resolution, say 1920x1080 pixels. Both have the same number of pixel to cover different areas. It means the biggest have to use either bigger pixels (less likely) and/or bigger space between each pixels, resulting in a "fuzzier" image). It's not something you'll notice right away so don't be concerned too much about that, but it's good to know.
Choosing between a 1080p and 720p:
In your case, it's easy to say go for a 720p; It's actually going to be better with a 720 than a 1080 (you might even regret a 1080 with no HD sources at hand). To explain, if your TV signal is SD (which is in fact 480i, much smaller than an HD source), the TV will have to scale the source (the picture) to match it's own resolution. And scaling equals distortion and/or blur in picture, and you don't want that or the least possible.
In terms of available technologies, there's two big players: LCD and Plasma.
Nowadays, plasma may be a bit cheaper than LCD (it was the opposite a few years ago). Plasma has much much better contrast ratio and deep blacks than LCD. However, it is super easy to end up with burn-in in the picture that can last from 15min to 2-3hours, and that's not really good.
Burn-in occurs when part of an image stay the same for a certain period of time. With plasma TV, burn-ins are rarely (never?) permanent though, it's just way annoying because you see a "ghost" of that fixed image overlayed with the real picture you want to see. Now just think of the two horizontal black bars when listening to movies: you watch a movie for 2h, then the TV-> with two semi-transparent black bars on top and bottom of the screen, nice!
LCD don't have that problem at all, and usually last longer than Plasma (plasma burns gaz while LCD is made of diode that can last tens of thousands of hours, if everything goes well).
So I'd just say, stick with LCD. Plasma is good for home-theatre dedicated rooms that you don't use as regularly as say the living room.
Contrast/Brightness etc
1st thing 1st -> a 10,000:1 contrast don't exist in LCD *AT ALL*. You'll see plenty with super high contrast ratio but that's just number on a sheet of paper backed by the process of changing dynamically the brightness of the TV in accordance to the picture shown (it's called Dynamic Contrast because of that) and it's not very pleasant to watch.
If the number you see is around 800:1 to 2-3000:1 chances are that this number is more realistic. The higher the better (deeper blacks/brighter whites)
Refresh Rate:
Usually something between 2ms to 8ms. The smaller the better. 8ms might be considered bad but it's actually pretty decent if the TV is of good quality.
Most TVs have pretty decent refresh rates now so that shouldn't really be an issue.
Inputs:
Make sure the TV has enough inputs for your needs, and of the good types. They usually have more than needed but take a look just in case
Brands:
Few companies make their own LCD panels. A quick search on the web should tell you which ones exactly. I'm really not sure about who makes them or not, I used to know when I was salesman but that's a while ago and things changes.
IMHO, Sony tends to be overpriced in almost anything. Good brand, great products, but you pay a nice premium for the 4 chromed-plastic letters on the front of the TV.
Sharp is, I think, the best compromised in term of quality/price/service. When I searched to buy mine, I went with Sharp as I found it was the best option there was.
LG, I'm not sure what to think about them. They're not as big as Sharp or Sony, they've got less experience in TVs but they started with computer Monitors way back then. I've heard good things about them though so I guess I wouldn't mind having one. If budget is critical but you want a lasting TV, Lg would be a good choice.
White Westinghouse, Insigna, Phillips, Daytek (typo?), and so on:
While they're inexpensive, chances are that these TVs die on you under 3 years. I personally think it's not really worth the prices unless you get a really good deal. Not to mention the quality will suffer. These constructor buys their lcd panels from the big players and make a frame around them, puts cheap electronics to drive the LCD and backlight so the result is usually not so good.
I think that's pretty much all there is to know about TVs
If you've got other questions and stuff you're welcome to ask
I suggest you take a look at this too:
http://www.lcdtvbuyingguide.com/lcdtv/lcd-tv-contrast-ratio.html (look at the rest of the site as well)
Also, if you need cables and stuff, buy them online. You'll end up paying around 10% of what they ask in store. An HDMI cable in store can cost nearly a 100$ while online you'll have the same thing for around 10$.
Hope this help! (I know it will

)
O.
edit: Wow now I realize I had nothing to do at work today! lol