Hi, and congratulations! I thought UK residents were excluded from the Green Card lottery (or maybe it's UK citizens...) The US is a mighty big place, and very often the private sector "public service" providers you are asking about are specific to a particular region, state or area.

>>Broadband Providers in US? (like UK: tiscali, sky)<<

Depends a bit on where you are in the US - but many of the phone providers also do broadband - Verizon, AT&T. There is also the possibility of getting your broadband via cable (see below under TV services).

>>TV services (like sky, virgin)<<

Cable TV is still limited in the US to a single monopoly per town. (In NYC, the cable franchises are laid out by neighborhood - but there may be some providers specific to the building you live in.) If you're in a Comcast area, you get Comcast cable, for example. There is satellite tv in the form of DirectTV (hit any Radio Shack for info on the dish and subscription rates). Some towns restrict the size of the dish you can use, and some won't allow you to put it anywhere it is visible from the street.

>>budget airlines (like easyjet, rynair)<<

Southwest, Jet Blue, there are others - again, it depends a bit on the region

>>money comparison sites (like moneysupermarket)<<

This is a new one for me. Not sure what you mean here.

>>Online Banking? can we open a bank account online?<<

There are plenty of online banks - but regular banks let you use their online services to do just about anything you like (transfers, pay bills, etc.) free of charge. The other "interesting" thing is the banks that are set up in supermarkets - open all hours, and many open on Sundays.

Big national banks include Bank of America and Citibank. Again, many large regional banks.

>>Landline providers? (like BT)<<

Verizon, various successors to the "Baby Bells" (what was the old Bell Telephone network after it was broken up), again, it tends to be regional.

>>Mobile phone services (like orange, virgin)<<

Verizon, Sprint, AT&T, T-Mobile (the old Deutsche Telekom) - most offer package deals that include landline and mobile services.

>>Supermarkets (like tesco, asda, sainsbury's)<<

Regional - in the Northeast, Stop & Shop, in the Midwest, Kroger, in the West, Safeway (not related to the UK chain - or at least I don't think so). Whole Foods and Trader Joe's are upscale supermarkets and pretty much nationwide these days.

>>Water/Gas/Electricity suppliers?<<

Regional and "deregulated" these days. (I.e. privatized) But there is very often a choice - at least in the electric and gas markets. Water is more or less by town or region.

In most areas you're spoiled for all the choices. And everyone advertises like crazy - on television and in the newspapers. It might almost be easier to pick a major city you'd like to be in or near and start scanning their newspaper online. You'll get a feel for the various services, brands and the local issues concerning the various services.
Cheers,
Bev