First thing is there there is no straight answer. There are so many variables and factors that may dictate how each person can or has to do.
There are your local weather, land charactoristic, predators, etc. There was a keeper that picked a nice shady spot but realized that it was too far to run electricity when he needed to plug in water warmer came winter. Another found that the coop was built on a low spot that the run was always muddy.
Then there are your personal preference, such as flock size, cost investment, maintenance plan, free range, etc. Some people like to walk in to the coop to collect eggs while some like a outside access door.
And there are the chickens natural habits. They want to roost at the highest spot. They like to stretch the legs and flap their wings. They like dust bath. They poop all the time. Their egg laying fluctuate with amount of lights and other stress.
If you want a mobile coop and still have ample room, consider building a coop on trailer. As you plan your build, plan your design to be flexible and easily modified, because you likely will see room for improvement as along the way.
As for coop height, my coop ceiling is ~20in (not an absolute number) higher than the highest roosts. My coop (3x6x5) is a lean-in as oppose to walk-in. I can reach in and touch every corner. It has been a good home for 9 birds. It is portable to a degree. The roof lifts off and the two parts can be carries by 3 to 4 people. PS, the roof is covered with sheet metal, much lighter than asphalt shingles.
