Thanks for the responses so far. Here's some more info for you.
The TV needs to fit here -- this is an old picture, but it's the same TV and stand:
The stand is 2 feet deep. I am not going to replace it because it fits perfectly in the room and also functions as a speaker stand.
I don't need a larger TV because we sit between 8 and 10 feet from the screen (depending on where we put the couch).
I also don't want to spend a wad of cash. Since we're trying to save up for a house, that's the priority. (And yes, every $500 counts.)
That being said, I think I can safely cross HDTV-ready off my list of desired features. To take advantage of it would require more new equipment besides the TV, anyway.