Wait, you have a 1080i or 720p? or can it be both?
I think I've tried to process too much of this stuff too soon.
It may be confusing, no doubt.
When you hook up to cable, your TV will receive SD (regular TV) signals, and HD signals in various formats including 1080i and 720p as well. It depends on the source! HD Sports tends to be broadcast in 720p, while Mark Cuban's HD Net broadcasts in 1080i. The TV, if capable, will show them all.
If the TV is 720p, it will resize a 1080 picture on the fly, much like how you can resize an image in a paint program.
The signal can be 1080 but the programming can still be SD. This makes sense if you consider that it's the signal that's HD and the signal is what matters. What you will see in this case is vertical bars on the left and right of the SD picture. These bars can damage some TV technologies (projection is one) if you watch lots of hours of TV with those bars on the screen - it's called burn in. The benefit of an HD signal is that the color information for all the dots is sent digitally so you get perfect colors and you don't have to do any adjustments on most TV's (projection you have to adjust convergence).
If you're comparing two TV pictures, and you can ask the sales guy to show Discovery HD Theater on both, you will be getting the same source and about the best picture quality available.
Something not mentioned yet is the sound. For a long time before HD was available, they've been making advancements in the sound. Many programs have Dolby Digital 5.1 sound tracks; if you have a nice sound system with front and center and rear speakers and a subwoofer, the audio effects are pretty amazing. You'll hear a helicopter fly from the rear to the front, or the music soundtrack from the back and the talking from the front.
If you don't have a sound system, then the sound put out by the TVs is something to compare, too. Many of the sets with awesome pictures have horrible sound - the sound isn't an issue if you have a sound system.
You mentioned HDMI. If you have XBox and PS3 and a cable/satellite receiver that all do HDMI, the TV needs 3x HDMI in if you want to use the TV to choose between them. Or you can use 1 HDMI for the PS3 and other kinds of video connections for the other sources. The newer sound systems also have HDMI and you can select the sound/picture sent to the TV using the amplifier; then only 1 HDMI on the TV is needed. Going forward, the more HDMI inputs the better!
HDMI does nothing for the picture that DVI won't do. The real benefit of HDMI is that it packages the DVI picture signal with the advanced audio signals in one cable. And some of the newest audio signals require the DVI connection.
Yeah, I know I'm putting a lot of info out there. Take it all in and use it for whatever benefit you can.