We *just* signed a contract for this. We chose to do truck on site shredding so we could examine the truck and determine that they completed our work.
Absolutely on signing a contract, this is highly confidential stuff, it's not the cardboard recycling from employee snack and amazon shipments, it's bank records. I'm about to draft a procedure on it for employees in the locations using it to sign off on. Daily shred from your stations goes to the locked bin, (no BSA management stuff gets shredded by the vendor, no Board stuff gets shredded by the vendor, etc.) as well as the step about confirming that all the records were destroyed onsite.
I read the contract to determine their hiring and certifications, and for typical vendor management things. My operations manager contacted people for service records (including people that we knew used them that weren't on their list of clients/recommendations.), and one of my loan folks reviewed their financials.