Search this site for for trip reports/videos by "blindwilly". He and his overlander crew have made several trips to the area. I'm sure he'll chime in soon enough.
I will chime in now, lol.
Sorry for the delay, I was on vacation in Sedona.

You will encounter pin striping. Once you realize that, you'll enjoy the trails and campgrounds in BBRSP.
Camping with extra vehicles in the park pretty much requires group sites or equestrian camp sites. My last trip in Dec 2019 I started with 6 vehicles planning to go, so we chose equestrian sites. We ended up with 3 rigs and lots of space to camp.
Javelin campsite was one great spot for all of us, Tres Papalotes is another.
One option to consider is the private ranch's/campgrounds near the park. They have both primitive and glamping facilities.
(Los Alamos Ranch and Rio Bravo Ranch come to mind)
The NW side of the park is the roughest, also in spots VERY prone to pin stripes. (Chapaduro spring, and Ciennega Creek on the south end of the Ciennega loop, and the area around Cat Spring). However, it has the best wheeling, is the least populated and some incredible views.
In the main park has some great trails also. I haven't been on all of them but the ones I have been have been great.
Paseo Al Solitario is the roughest one I've been on to date. After that would be the area around Oso Loop and Rancheria Loop. (You can reach that via the Javelin Pens campsite)
Botella Trail was a FANTASTIC surprise of a trail. I was expecting it to be scary and it wasn't at all. There were a few technical spots , lots of dry creek beds, some hills and one giant boulder! I here there are 2 sides to that trail, a west and east trail. We did the East trail.
You can't think of BBRSP without the Road To Nowhere.

Under normal conditions, it's an easy trail with steep drop offs, great views and is a narrow 2 track. There are also some tracks up to the mines on that side of the park. Lots of fun in the Solitario!
Hope this helps!
1st photo is at the Cienega Gorge.
2nd is in the middle of Cienega Creek. It was overgrown from all the rain the previous years. You'll feel like you're loosing ALL your paint, but you won't be...