To me, the benefits of plasma outweigh the negatives (as well as the benefits of LED/LCD) if your situation warrants it.
The first thing I'd ask is where you'll be watching your new set. Plasmas, being a glass screen (instead of the moulded plastic of LED/LCD), are susceptible to glare, particularly from the sun. If you have curtains or lamps placed in a way that won't hit the screen, you're golden. If not, I wouldn't recommend plasma at all.
A second drawback to plasma is the issue of image retention or screen burn-in. If you leave your TV idle too long, the pixels will retain the image left on screen. Everyone always says "Well, I won't leave it on the same screen for hours on end", but think about something like a score in the corner of a screen during a ballgame, or a stock/news ticker. It's relatively easy problem to solve (leave a blue or snowy screen on for the length of time it took the image to burn in), and plasmas may have progressed in this area since I left retail in 2008, but if it seems like a headache, go with LED/LCD.
Finally, plasmas are both heavier and much worse on power than their counterparts.
On the bright side, plasmas do a much better job reproducing colour (particularly blacks) and have a wider viewing angle than LCD. LED combines the benefits of both plasma and LCD, but, as you mentioned, at a higher cost. Plasmas are cheaper now more than ever because LED has become the market leader.
Another thing you mentioned was choppy images. This is measured in HZ. Most LCD/LED's offer either 60 or 120hz (meaning the image on screen is re-drawn 60 or 120 times per second). Plasmas offer 600hz. Apart from Jeopardy!, I only really watch sports, so the benefits would be great for me, but the last time I was looking at TV's (when I helped my grandparents purchase their set in 2009), I noticed a huge difference from 60 to 120 watching Conan O'Brien deliver a monologue - he was, well, being Conan: Moving his arms about, dancing, etc. The judder from something as simple as talking with his hands was noticeable.
Hope this helps!