The basic competing tech is LCD and Plasma. LED is a back lighting method for LCDs; plasmas don't use backlights as far as I know.
Of those two, LED is more common and has no screen "burn in" issues, plasma is cheaper and has better blacks and hence contrast ratios (due to no backlights), but does burn in if you leave a static image on it too long (or something like a logo in the corner of a TV station screen). Burn in is probably less an issue for newer Plasmas, but still a concern, depending on your usage (e.g. video game playing with a game's HUD). There are much fewer plasmas and the tech tends to be less "advanced" than LCD, in general, as far as fancy features supported, etc. Also I think plasma still tends to use more power. The upside of plasma is basically you can get the same screen size and resolution as an LCD, usually for cheaper, and with potentially better image quality (depending).
Go for some form of Internet capability if you want to, but basing much of your decision on it seems foolish to me as almost all of this tech is limited (not a general "You can do anything a browser can do, but on your TV!). The better solution in my view is to hook up a nice little HTPC and then you truly get all capabilities. Plus, who wants to type URLs on a TV remote?
Now if you're talking about *media streaming* support (DLNA, etc.), that's different, it actually has little or nothing to do with Internet support, per se (except that they're both network-based, of course). And in that case yes it can be useful, unless you have the previously mentioned HTPC. Bottom line is I think getting a "dumb TV" with a "smart computer" attached to it is going to give you way more long-term flexibility and capability than any other option. But if you really don't want to deal with an HTPC, don't want to spend the extra money, don't have space in your AV space, etc. for one, then I guess try to get as much of that stuff built-in as possible. Just keep in mind that the industry is in flux and a lot of stuff that's supported now may not be supported in, say, 5 years, and if you're planning for a 10yr lifetime, well... then again you can always buy an HTPC and add it on to any TV you get.
The other thing to think about is 3D. I personally dislike almost all 3D media and technologies I've seen so I wouldn't bother and it tends to add to the price anyway. If 3D is important to you, you might want to wait for better tech if at all possible. I would basically suggest not getting 3D (and saving money), and then buy something new in 5yrs for 3D if you really want it.
I know that's not a comprehensive answer to everything you asked, but hopefully it's somewhat useful.