I live in the UK and this is my first posting on this forum.
I have also just bought a new 32" Philips HD LCD TV, which unfortunately is not as good as the one you were looking at as it is not '1080p' nor does it have anything like the number of pixels or screen size.
My answer is a bit long but I hope it helps
In relation to your question, 'Media Connectivity' is not a term I have heard used here. I would assume it would be something to do with connecting to media, in other words connecting to media devices e.g. DVD players/recorders, vcr's, computers, and game consoles - Microsoft XBOX or XBOX 360, Sony Playstation - camcorders, etc. using either the red, yellow and white phono cables, scart, rgb(component), or hdmi cables or whatever other connectors BOTH TV AND DEVICE would have to have.
The terms NTSC refers to a technological format used by the US TV broadcaster i.e. in the UK our TV is broadcast in PAL, Japan uses SECAM?, USA uses NTSC. This is also the same for anything 'recorded' in these countries e.g. if you recorded some tv at home in the US then took the vhs tape with you to some freinds or relatives in the UK or japan it would NOT display properly if at all in their VCR, and also if you brought a vcr and/or tv with you from the USA that also would not work even if you had an adaptor for the different electrical plug that the US uses, though some TV's like my old one can switch the from NTSC to PAL and vice versa, ascould my old vcr but hy are both now worn out. Just how this would relate, if at all, to the presently available and the new and upcoming HD (and blu ray) DVD players/recorders, I don't know.
You should also be aware, if you are not already, that the US and other countries all use 'region coding' technology in DVD PLAYERS, Recorders and games consoles, and on the PRE-RECORDED DVD's and games that they use in them, that is supposed to prevent people in the UK and other countries from getting their hands on movies and games that are released on DVD in the US, before those movies are even released to the Cinemas/Stores here in the UK. e.g. UK has 'region 1' so DVD's from US will have a different region coding initially, until the film studios decide to release versions that UK and other countries DVD players and games consoles, can play. To get round that you could always look for a player that is 'multi region' coded. The same will also be true for pc's, I expect that can play games and play/record onto DVD.
As for ATSC, QAM, (and 'i' and 'p'), as well as the difference between them and what they actually mean, I have no idea, as I have never heard of these terms, but if they are in the same location on a card showing the details/features of a TV (that you ARE familiar with or the assistant has heard of one of the terms quoted), then would also assume them to be refering to something similar, i.e ATSC and QAM would be some other broadcast format and the relevance of 'i' and 'p' would be connected with picture quality. I think if the 'p' means progressive it could be refering to something like 'progressive scan' which is something used by higher quality vcr's to improve the image from analogue vhs tapes, so how it relates to a HD TV I am not sure but it might be related. The 1920x1080 refers to the number of pixels that are used to make up the image on the screen, therefore the more the better, just the same as it is with computer monitors (which your new HD LCD TV will be able to be used for, if it AND the pc has the same and correct type of connectors) and digital cameras/camcorders.
Also a lot of features on these and older tv's may be useful as away of gauging quality, but like you said you don't know whether they are defined by the TV or the broadcaster. All of the features you mentioned are inherent in the TV's, but to make use of some of them like High Definition or Digital the broadcaster has to be broadcasting their content in high definition and/or digital.
In the UK our choices are terrestrial analogue TV (or terrestrial digital which uses a different kind of tuner/receiver NOT found in VCR's and older CRT tv's) through an aerial or digital only via a digital 'cable' receiver/decoder or fixed satellite dish and receiver/decoder. Only the 'Satellite TV' company here currently broadcasts any 'High Definition' content - which is more expensive than 'ordinary digital' - on a low number of channels, so currently we have no real 'need' of 1080p at the moment.