Plasmas aren't without their drawbacks: They are susceptible to burn-in if not broken in correctly and they run hot, which can easily heat up a smaller room quickly. They are also less energy efficient than LEDs, they have more reflective screens making them less ideal for brightly lit rooms, and they're heavy.
Having said that, however, if you're going for the best picture quality (which is imperative to me personally), plasmas are better than LEDs and leave standard LCDs in the dust. They have wonderful contrast ratios (light to dark aspects), excellent motion detail without the lame "soap opera" effect of 120/240Hz LED/LCD, and an unmatched off-axis viewing angle, meaning the picture quality does not falter if you're not sitting directly centered.
In short, if you can live with the heat they produce (it is a gas-based tech) and you break them in correctly to get them past their initial image retention and potential burn-in problems, then plasmas produce a better looking, more natural picture at a cheaper price. I'd recommend a Panasonic Viera (now that Pioneer is gone). Samsung has good models too.
If you absolutely would rather have something other than plasma, then go for an LED backlit LCD with local dimming. I'd go for a Samsung here (Sony is good too).
Oh, and OLED, while beautiful, are far too expensive now or in the near future, and 4k res is not really worth investing in any time soon due to a lack of native content. Unless you want to PC game with a good rig on your TV, I'd stick with 1080p for now.
Here are a couple of links to help you out:
http://www.soundandvision.com/content/do-you-prefer-plasma-or-lcd-tvs
http://www.soundandvision.com/content/should-you-get-lcd-or-plasma-flat-panel
