First of all, I don't consider myself an expert on HDTV's, but I just bought one for Christmas and did a LOT of research before purchasing.
From what the OP said he will not be viewing any sort of HD content (SD channels, DVD, Wii) so 1080p makes no difference. However, 1080p is somewhat future proof in that if you decide down the road you want a Blu-Ray player or a PS3, you're all set. Keep in mind that a lot of the standard def stuff you watch will look worse than the CRT set, in some cases much worse. Some of the lower quality standard feeds are like watching an old VHS tape on a regular TV. I would highly recommend getting at least a Blu-Ray player, you won't be disappointed.
Some TV's are definitely better than others at upconverting standard picture feeds. The lower end TV's will make standard def look awful, the higher end models will make it passable. Some Blu-Ray players are also better than others at upconverting, making DVD's look pretty decent.
Also keep in mind that with TV's, the 400 dollar Sony at Wal-Mart is not the same as the 1200 dollar model at Best Buy. Sony, Samsung, and similar name brands will often source their low end models from the same Chinese factories that make generic no name models. So a low end Samsung actually isn't a Samsung (which is a good brand) at all, just a generic knock-off to match a price point.
Finally, don't think that as soon as you plug it in and turn it on, that's as good as the picture gets. Go to Google and type in "(Brand Name)(Model Number) Calibration" Often times you will find someone post settings from a proper professional calibration.
Another thing, don't get robbed when purchasing cables at the Big Box store. The markup is insane, and gold plated triple coil platinum core interference wound blah blah are no better than the cheap ones. Go to monoprice.com, and watch your jaw drop when you realize you can get a 6ft HDMI cable for a few dollars.
