Since this board is for American style "backpacking," which to you is wilderness trekking, it's probably not the best source for information, although most of us have done both types of "backpacking." You might have better luck with a travel board like Lonely Planet's Thorn Tree. It has gone a bit downhill since the BBC took it over, but you can still get good answers to most questions. Their FAQ for the US (although horrendously long) is excellent and worth wading through. You are more apt to get help there if you search the site first, read a guidebook and then ask specific questions rather than the general ones you posted here. Questioners who haven't done their research tend to get flamed on that board.

A couple of things to keep in mind: Most US National Parks cannot be visited via public transport (Yosemite and the Grand Canyon are exceptions), so getting there requires either a tour or a rental car. Probably 99% of campgrounds in the US cannot be accessed without a car. It's a lot different from Europe where campgrounds are located close to or even in cities. Here they are generally far out in the countryside.

As TomD suggests, a guidebook is a good idea. Note, though, that food and (because of the soaring price of oil) transportation costs have inflated considerably this year.