The parks are very popular, especially in peak season but you shouldn't have to much trouble finding quiet spots off the beaten path away from the crowds. If you have no luck with camping look for lodgings in Springdale, it's a lovely town and the free NP shuttle bus runs from town into the canyon, which is the only way to get to the canyon area.

Between Arches and Zion you have could take a very scenic drive along UT24/scenic 12 and make quick stops at two more incredible parks, Capitol Reef and Bryce canyon with time permitting. [??] If you end up visiting 4 or more National parks this trip, or in the coming year including this trip, the you will find the annual parks pass for $80 good value.