Timberland has provided the most thorough and correct answer. The only thing I would disagree with is that if you are going to purchase a TV, don't purchase anything over $300 that isn't digital and HD ready. You'd be wasting your money.
I live in an area where most of the stations broadcast in HD as well as NTSC. Don't worry, your old analog sets will work for years to come precisely for this reason. HD broadcasting equipment is an add on, they aren't going to throw out the NTSC equipment and lose 90% of their viewership overnight. Trust me on this.
Most HD sets currently sold do not contain an HD tuner, you have to buy it separately. Currently, most HD signals are broadcast over the airwaves. DirecTV only offers a few signals in HD, and none of the satellite feed "local channels" are. You need a good antenna. There are HD tuners than can handle both antenna and satellite signals so you only need one, and they are dropping in price. It's still expensive, and you need a special dish too, so, unless you really want to watch the Sopranos in HD, the ideal setup right now is an antenna, combo sat/ant HD decoder (for future sat use) and a standard one or two room dish.
You can now get a very high quality HD ready set for about $2000, which used to be the break in pricepoint for big screen TV's. If you'd like specific recommendations let me know.