I decided I wanted a full-HD 1920x1080 flat panel, which pretty much limits it to LCDs.
At the 40" level there is the Samsung LN-S4095D for $1900 online ($1400 at not-so-reputable places, $2500 at Best Buy.) Other alternatives are the Sony KDL-40V2500 ($2000-$2500), Westinghouse LVM-42W2 ($1400), and Toshiba 42HL196 ($1700, $2100 at BB.)
The Samsung looks like a very nice box, and has a dedicated game mode. The Westinghouse has some bad reviews, and only has one composite input (I need two to get started, though with that amount of savings I can just get a new DVD player.) It's also only got a single HDMI input (but two DVI inputs) which is a bit limiting.
At 46" the Toshiba and Sony models are a bit pricy, so it's either the Samsung LN-S4695D ($2400 at Amazon, pretty cheap even compared to random stores on Froogle) or the Westinghouse LVM-47W1 (just $1900 at Best Buy.)
I will probably take a quick trip to Best Buy tomorrow to try to see some of these in person before committing.