There are numerous types of background checks you can run for sensitive positions. I recommend at least doing both a criminal and professional license/education background check. You mentioned transportation, so I mentioned the licensing check for any drivers or other transportation personnel who will be handling regulated materials that require a license or certification to manage. You can also do an e-Verify check if you want to ensure the employee is eligible to work in the U.S. (although the I-9 process is designed to help with this.)
Check out our article on the Best Background Check Companies if you need a company that can give you numerous background check options with a quick turnaround time.
Let me know if you have any more questions!