I hate to say it, but HDTV may not be your answer. If your picture quality with ATT digital cable "sucks" on your 27" TV, it will look even worse on a big HDTV. Digital cable has nothing, and I repeat nothing, to do with picture quality. It is a way for the cable company to get more content onto the bandwidth they have and nothing more. If your cable company is really interested in picture quality, they can work on it. Most don't care. They advertise digital because that has become a buzz word for better and improved. In reality, it isn't.
If you want HD quality, you are going to have to spring for an HDTV and probably some type of set top box (STB) receiver that will combine over the air (OTA) and satellite reception. Depending where you live and what satellite you tune into, you will get 2 to 7 or 8 HD signal sources. Some cable companies are now offering HD over cable, but these are few and far between. You might check with your cable company about that, but it is a separate service from digital cable.
DVDs also look great on an HDTV (whether progressive or not), but sadly regular cable, digital cable, OTA non-HD signals, and regular satellite signals will often suffer.
SMK