We've had our 40' MH for 10 years full-timing. Our first choice is always a public park - national, state, national forest, county, city. We have 6 different national forest campgrounds lined up for us to stay this summer - in Arizona, Colorado and New Mexico.
We do our homework beforehand and have never failed to fit in the parks we choose - most often without reservations. You won't fit into every park but there will always be another one nearby that you will fit. Private parks would be no concern. We also mainly travel west of the Mississippi but have done a lot in the east, also. We have stayed in major parks - Yellowstone, Grand Teton, Glacier, Rocky Mountain, Zion, Bryce, etc. so it's really not an issue. Get the RV that you feel comfortable living in and just go!!