National Parks, State/Provincial Parks, selected City Parks and then private are the basic order we follow. However, there are always exceptions. Specific places may not have any public campgrounds or they may not have the hook ups we desire at the time.
Our priorities are (1) where we want to be (2) scenery/animals (3) 50 amp (4) Satellite TV signal (5) WIFI (Verizon is my phone carrier and they seem to have the best overall coverage) and sometimes (6) long pull thru site.
For one-night stands when we don't want to do a rest stop or parking lot, pull thrus are so much more convenient AND when we are hauling the enclosed trailer with a car they are virtually a must.
We seldom stay any specific place longer than one week so monthly rates are not important. We aren't full timers but we regularly take extended trips for 3-4 months during the summer.
As folks have said, you must decide what is important to you (and this may change with different trips) and then select accordingly. Have fun and enjoy.
Diann