Consider winning the war instead of only the battle ;)
I've had similar discussions in the past when helping friends/family upgrade their older TV rooms. Ultimately, you should seriously consider a new HDTV stand as well. Why? Because not only will this give you more flexibility in the HDTV you take home, you gain the proper viewing angle that (long term) is better for your neck/back/eyes. Since most people do not upgrade their TVs very frequently, it may be worth it to think longer term with your new HDTV/furniture. Luckily, TV stands are not expensive. Target/Ikea/etc. have decent options.
Basically, 60" is too tall to place your HDTV. [Exclude the folks who find it acceptable to mount an HDTV over a fireplace. Different discussion.] Ideally, it would be a lower stand with your eyes (while looking straight ahead from the seating area) focus on the top portion of the HDTV.
FWIW, a 32" HDTV won't fit into the same (square) space since it's wider than your old JVC standard definition TV.
Anything smaller is not really worth it at a 12' distance since in the smaller sizes, all HDTVs will be seen the same (variations of color aside)/resolved by your eyes/brain similarly. See chart for reference:
You should consider moving your seating area much closer to the HDTV if you end up with a 30" or less HDTV so you can see all the detail. Less than 8' would be better.