What is the most logical next event?

How to keep your home free of rodents
Clean the crawl space.
If you've got rodents, you'll see the insulation hanging down (they like to nest in it) and droppings on the vapor barrier. If it is bad, get rid of both.
Once the area is clean, you can see what needs to be done. Rodents can carry some nasty diseases (hantavirus for one, but it is rare) so you may want to wear high-quality respiratory protection.