While the current TV set receives well, it does not receive HD. (No kidding - I'm pretty sure HD was not around in 1995.
Without reading other remarks:
Plasma is on it's way out; while you may be able to pick one up for a song, be sure to check it's energy efficiency. They got a reputation for being energy hogs for a reason, but not all are. Still, the reputation for that and burn-in killed the market, the last major maker is getting out of the business now.
LED is actually LCD with LED backlighting, as opposed to CCFL(a specialized type of flourescent light). It allows LED TVs to be thinner and even more energy efficient.
If you're putting it on furniture, I'd take a look at what said furniture can handle. How wide is it? How much overhang can you stand? How far away do you sit from the TV? The benefit to a larger TV is that you can still make out the additional detail from further away. Apple has branded 'higher than average human acuity' as 'retina display'. Much like MOA, humans are restricted to about 1 minute of arc (1/60th of a degree). So as the resolution goes up, the closer you have to sit to see it. SDTV is 480, HDTV is 720 or 1080. Each step has 50% lines of resolution(and 2.25 times as many dots/pixels) than the one before it.
Translation(after some trig to convert 4:3 to 16:9): Whatever distance your 27" screen is at, you'll need a ~50" TV to keep the pixel sizes the same at 720, 75" for a 1080. I'll note that at 'Standard Definition' a 33" screen will give you the same height as your old TV. If you already sit too far away to see all the detail(will moving closer to the set let you see more detail right now?), you won't see all the detail at my quoted sizes. If you sit close enough, the bigger screens will indeed let you see every bit. Buying a higher resolution screen now generally doesn't cost more, and if you can't see the detail, oh well. If you want you can always move closer, which isn't an option if you didn't buy the higher resolution in the first place.
Another reason to go bigger is that bigger screens moves the 'optimal' viewing distance further from the screen, allowing more people to see it.
Technical Jargon? I'd look for a 1080 capable set(with 4k types coming out it's no longer anything near cutting edge), Energy Star compliant(easy on your wallet afterwards), and enough inputs for any gizmos you have and/or might obtain in the future(probably not a problem). I'd check the viewing angles of any set you're considering - how far off center can you be and still see a good picture? Some LCD TVs are much better at this than others.
If you get a 'Smart' TV that has network options, that allows you to do things like watch netflix, youtube, and other such 'internet tv' services without additional equipment. In exchange, expect a more complicated remote. In which case what I'd look for is a RJ-45(wired network) connection and wireless-n(latest wifi standard). Some might only support G, but at this point I'd want one that's future-proofed in case I replace my router.
As for getting the wifi to it, you'd need a wireless router. Let me know if you don't have one. It's either that or if you get your internet via cable, you might be able to just run a network cable to it. Check for open ports(look like fat phone jacks).
As for hanging it off the wall, any set should come with a stand, you need to buy a VESA mount to put it on a wall, though some furniture comes with them today; I like the mount because it means your TV is NOT tipping over.
