Since you're going to be full-timing get a RV that you can comfortably live in 365 days a year. Also, if you're planning to spend time in the west you'll have no problems finding nice spots.
We have a 40' motorhome and yes, you can boondock at the North Rim. There are many, many other beautiful places in this country. Our first choices are always boondocking or public parks (national, national forests, state, county and even city). We truly do not have a hard time getting into those parks or boondocking areas but you need to do your homework. No, you won't fit everywhere but still, you'll have many possibilities.
You definitely don't need to drive far off the paved roads to find good spots so I disagree that you need a 4x4 or a truck camper. We take our motorhome on unpaved roads but again..you need to investigate the area before you take off.
Again, a full-timing RV should be your main concern because that will be your home. Good luck!