480i is pretty much 'analog'
'Anamorphic widescreen' or 'Enhanced for widescreen tv' DVDs are 480p, p = progressive, it still writes 480 scan lines, but 2ce as often as 480i [ interlaced].
720p is sometimes called HD, but is probably closer to ED [enhanced definition]. I would not suggest getting a tv that only does 720p.
1080i writes 1080 lines of resolution, every other line at a time [progressive writes every line at a time.] The pixel count is something like 10x what is available for 480i [not sure if it's 10x, but it's a noticeable increase].
There are upconverting DVD players or TVs, but I don't know much about them.
Most HDTV signals [cable, satellite, antenna], are at least either 720p or 1080i. My tv is 480p or 1080i, but i can tell my cable box to output only in 1080i [this doesn't upconvert, but it does send the signal in a format my tv can understand.]
HDTV broadcasts, done right, look *incredible*, like you could reach in the screen and touch it. I've had an undersea thing from Discovery HD on the DVR for months just because it's so cool to look at.
The issue, of course, is what content can you get now and in the future? I'm getting the networks, HBO, SHO, and Discovery in HD, and of course am waiting for more.
DVI isn't an industry standard, and you will find various levels of support. My tv and my cable box both have DVI, but it's not active on the cable box, so I'm using component cables.
You will see an improvement on anamorphic dvds going from 480i to 480i, but it's most re: the color depth/separation [more detailed and crisper colors]. The jump from 480i/p to 1080i is breathtaking.
Re: HD video games: check out hdtvarcade.com
If your tv is dying, and you need to replace it, I would definitely get an HD-ready tv. If you have cable, lots of times you can upgrade to an HD box for no or little add'l charge, and more things are going to go HD in the future. If you don't have cable, you can get a set-top box and antenna, and get HD networks free over the are [check out
www.antennaweb.com for information.]