Screen burn is not an issue anymore on the latest plasmas, but it would still not be ideal to have a static graphic on it 90% of the time, so if you always play one specific game with a score or health bar etc. sitting in the same spot then LCD is maybe the better option.
For TV/movies no LCD will give you the natural picture that a good plasma will ... with a 17K budget you can get a Panasonic FullHD 42" plasma. At that size FullHD is REALLY not important, but it does have one major advantage:
Anybody who sees your new toy will immediately ask "Wow, now tell me, is it one of those new FullHD/1080p models" and you can then honestly answer "Yes", instead of having to explain that it makes no diff unless you view a 50" from less than 2.5 meters away.