are standard definition resolutions not HD. HD starts with 720p and goes to 10801 and 1080p. So you want a 720p/1080i TV at a minimum. 1080p would be ideal if you have the money and are getting a screen at least 50".
As far as HDMI cables go they are all basically the same. You should get cables that are not so cheap that they fall apart, but you do not need $300+ gold plated Monster HDMI cables. When you are dealing with analog cables like component, S-Video, or composite, then getting super fat gold plated expensive cables can add some picture quality improvements. But when you are dealing with digital cables like HDMI, there is no difference. Analog is a wavelength. It's strenght of signal varies and can be affected by outside interference. Digital is 0's and 1's. There is no variation. It is either on or off. If you are getting a signal you are getting the signal, not part of it. Again the only concern should be that you spend enough on the HDMI cable (I would say in the $30 and up range) that it is well amde, does not fall apart, and does not fit so loosely in the HDMI connector on your TV that it just falls out (I have heard of $10 HDMI cables doing that).
As far as a starter LCD that I would reccommend, I would need to know what you are looking to spend and what size TV you want and whether it is absolutely necessary that you get an LCD. There are plenty of Rear Projection TVs that will produce a better image than a lot of flat LCDs, especially if you are looking for a budget LCD. You could also get a 50" or even larger 1080p RPTV for less than a cheap, smaller LCD that will not have the same picture quality. It is up to you of course, but it is something to think about. Going flat is the cool in thing to do , and there is nothing wrong with that, but know that the TV will cost 50" flat TV will cost $1000 sometimes even triple that of a 50" RPTV, and not even be 1080p (All RPTVs nowadays are 1080P, not so with flat panel). You are basically paying $1000 and up more for the same or less PQ, just because it's flat. There are flat TVs that have better PQ than RPTVs to be sure, but you will pay an arm and a leg for those. And you definitely won't find a Vizio or a Westinghouse that will compare to an SXRD or some of the better DLPs.
CNet could give you a better idea about what Tv to choose than I can. Check out their reviews. It should give you a good foundation for which direction to go in.
I want to hook up my PS3 to a flat-screen LCD TV so I can enjoy the games in their glorious Hi-Def imagery. I also want to be able to view the TV channels that are available in HD, but I am confused.
(1.) What should I be looking for in an LCD TV? 480I? 480P? 720?
(2.) I have found a variety of something called HDMI cables for the PS3, some being quite expensive,... which do I purchase? Are there differences, besides the price?
In other words, I want to purchase my first LCD TV and watch channels that are currently broadcasting in HD. I also want to watch Blue-Ray movies and enjoy Hi-Def gaming thanks to my PS3. What resolution (for the TV) and what cables do I need? Lastly, I am looking for a "beginner" or "starter" LCD TV - something that won't break the bank, but get me up and running. Thanks for any help.