Where to Stay
National Park campgrounds can be more primitive than others but they are often fine. For me being actually in the park is ideal. Sites can be hard to get during peak season as some National Parks get millions of visitors each year. Don’t count on electricity and even showers are not always available. Sewer connections are even less available (not that I use them). In the western states, flush toilets may not be available – just vault toilets (outhouse).
After National Parks, State Park campgrounds are often my favorite. They often have as good of facilities (not counting swimming pools) as private campgrounds. Often, they have larger sites with more trees than private campgrounds. Some State Park campgrounds are quite primitive, though.
In Canada, provincial parks can be quite primitive (British Columbia), or some of the best (Nova Scotia).
Private campgrounds vary a lot. Some are luxurious and some are crowded with many run down trailers for permanent inhabitants. Caveat emptor. In general, spaces in private campgrounds are often tight and are less likely to have trees or brush between campsites. The better ones are also usually more expensive than National or State park campgrounds.
Boondocking or Dry Camping. This is camping off the grid – bring your own water, no electricity or toilet facilities. There is a good deal of information online for this.
BLM Land: There are large stretches of BLM land out west and the cost is minimal. Some BLM land even has facilities and the price is very low. I stayed at one place in New Mexico that had a picnic table covered by a roof with a vault toilet reasonably close. It also had a gorgeous view over a canyon.
National Forest land may also be available. This is easier to find out west than in the East.