OK, here's some web sites that you might want to check out,
www.satelliteguys.us,
www.dbstalk.com and
www.avsforum.com, all great sites about HDTV, satellite, cable, home theater.
First of all, if you get a set with a built in ATSC (new digital standard) you might be able to receive your local over the air digital signals by just adding an over the air antenna. To see what stations in your area are digital, where their transmitter is and what type antenna you need go check
www.antennaweb.org, plug in your address and it will let you know. While ABC, CBS, NBC, FOX, UPN, WB and PBS networks all have some HDTV programming, not all local stations have been upgraded to transmit HDTV signals, just digital.
As for your resolution question, 480i is the old analog signal, 480p is what DVD's use, 720p is used by ABC, FOX, ESPN while 1080i is used by the other networks. Now while there are all these (and even more are allowed in the ATSC standard) your TV will actually use only one of these standards and either up convert or down convert the signal to match what your display can actually process. The ROT is that 720p signals are good for sports or other shows that have a lot of motion in them while 1080i is good for all other. I don't want to get into the relegious debate on which is better 720p or 1080i, the other web sites that I mentioned have many discussions on this subject, IMHO, just get a display that looks good to your eyes and you can afford.
For your connection question, using composite connections (usually the yellow colored video input jack) or S-Video (small round jack) will handle only 480i signals. To get 480p (DVD), 720p or 1080i you need to use either component (three cables that have red/green/blue connections) DVI or HDMI. DVI carries only video in digital and HDMI carries digital video and can also carry the audio signal but some hardware only handles the video on HDMI not the audio. If you're getting a LCD, Plasma, DLP, etc then using DVI or HDMI would be the best way to go since your display is digital, but if you're getting a display that uses CRT tubes then component will be OK since the display processing analog signals anyway. Again, IMHO, use what looks good to you. I do say don't spend a lot of dollars on high end cables like Monster, especially for DVI or HDMI, not needed.
Got you confused yet?
OK, now the really hard part, go with cable, DirecTV (D*) or Dish (E*). Right now, both D* and E* are in a transistion period when it comes to HDTV. They are in the process of migrating from the MPEG2 compression standard to the newer MPEG4 standard which will allow them to broadcast more HDTV programming in their limited bandwidth. Also, in most locations at this time, to get your local over the air HDTV stations you'll still need to get an over the air antenna since both D* and E* are just starting to roll out the local HD channels via satellite. Even then, at this time all they are carrying is ABC, CBS, NBC and FOX. Also, both services will require you make a commitment to keep their programming for 24 months for D* and 18 months for E*. And for a DVR, D* doesn't even have one that will do the new MPEG4 signals yet (later this year) and E* has one that was supposed to start shipping today but reports on the net are that they've discovered a problem with it and they are going to have a very limited release for a few months. Plus both providers will require you spend $200 to $300 to get the DVR). There is also a very heated debate about both DBS providers downgrading the resolution of one ore more of their HD channels to allow them to fit more HD channels into their limited space, which effects the picture quality.
What I would recommend, until both satellite companies shake out their migration is to go with cable if available in your area. Cable companies will probably have a higher monthly cost then D* or E* but you don't have to purchase hardware and there is no commitment, get it and if you don't like it cancel. I'm currently a D* customer (and have been E* also) and recently installed Comcast cable again due to lack of HD channels that I wanted on D*. Yes, I'm paying more then with D* but I get Starz-HD, Cinemax-HD, TNT-HD and our local Comcast Sportsnet HD channel which D* doesn't carry. Our Comcast system has also started to simulcast the analog channels (channels 2 though 99) as digital so all the old problems with poor picture quality on those channels is greatly reduced.
Hope this helps and good luck.