Some questions on National Park sites

My DW and I would like to start full-timing in the future. We expect to do lots of hiking during the day and some work during the evening/night. We MUCH prefer to camp in less open spaces that feature its own picnic tables and fire pits. We are not really interested in RV parks in an open area full of RVs that look like parking lots. My DW loves burning firewood in private sites. Our plan is to visit all National Parks and sleep within the parks, even if there are no hookups. I do understand that most of the sites are built long time ago and are not RV friendly.

I went to the top 10 most popular National Park websites and found out that they have certain thresh holds on the RV lengths - at 25ft, 30ft, 35ft then 40ft+. Hence, I am making an assumption that by staying below 25ft, I'm opening myself with many options.

Given this, which setup would be most friendly for our desired plan?

- 1T SRW truck pulling a 25ft FW
- 25ft B+ pulling a 20ft trailer
- 35ft Class A MH pulling a crossover vehicle

Remember, privacy is high up on our priority list. Do they let any of the above setup camp on sites that are designed for tent camping with decent privacy?

Your feedback are much appreciated from those who are experienced in camping at National Parks!