Currently LED and LCD are the same type of television. The difference is that a traditional LCD uses CCFL as a backlight light source. LED LCDs use LEDs as a backlight. There's your difference. The LED lights help improve the contrast, color, and blacks of the LCD TV. But it comes at a steep price premium.
LCDs, of any kind, are inherently bad a fast motion. They suffer from motion blur (ghost trails). This is compensated for with 120Hz and 240Hz refresh rate TVs. And the feature does help a lot (though it doesn't entirely fix the issue). But again you pay a huge price premium for this feature.
Plasma has a near instantaneous refresh rate, so it is inherently great a playing back fast motion. Plasma will give you better blacks, color, and contrast over an LCD (even an LED). They are even cheaper than LCDs with all the fancy tech specs. Plasma is your best image quality.
Plasma mainly suffers from myths and misconceptions now. They do not suffer burn-in anymore. They work in high altitudes. They do not have short life spans (most are 100,000 hours, so better than most LCDs). They are no longer energy hogs, you can get energy star certified models now.
In terms of energy saving, no technology is best. You have to look at each model separately. There are good and bad models from all technologies. Anyone who just says all LCDs are better or all Plasmas are better doesn't actually know anything.
Cheaper, again, Plasma is cheaper if you consider the video quality. A 'comparable' LCD will be way more because you have to pay for LED and 120Hz/240Hz refresh rates.
TV size matters though. 1080p, LED LCD, 120Hz/240Hz refresh rate, and Plasma vs LCD are all dependent on size. If you're going 37" or smaller, than a 'basic' LCD will serve you fine. You don't get the advantages of all those other things in smaller sets. If you get some of the 'high end' tech features in a smaller set, hey great, it can't hurt. But its not worth paying for. The advantages of those things I've listed kick in around 40" and moreso 50".
For Plasma stick with Panasonic. They will give you the best quality bang for the dollar. If they just aren't you're cup of tea you can settle with Samsung or LG then.
If you do decide to go LCD, stick with the S's. Samsung, Sony, and Sharp Aquos are all your friend. Samsung is the leader of the pack though these days. But any of those S's will serve you well. You can also consider Toshiba and LG. OH, if you go with a smaller LCD, 37" or smaller, then look to Panasonic. They make really great LCDs in the mid/small sizes.