In Washington, DC you cannot ask about criminal history until a conditional offer of employment is made. Then you can conduct your check.
i would recommend that, if you don't have an in house Human Resources professional, that you hire one to draft a policy for you and set up a system, perhaps preparing and RFP and helping you choose a vendor. Keep in mind that using an third party to conduct the checks requires conformity with the Fair Credit Reporting Act.
That being said, you should consider what level of checks you want for specific classifications of employees/volunteers. For example, certain states require child abuse clearances in addition to criminal background and FBI clearances for anyone working with children and certain executives. Others prohibit credit checks for certain jobs such as retail. So, you really should not tackle this on your own!
Here is a resource for you:
https://ohr.dc.gov/page/returningcitizens/applicants------------------------------
Roslyn Schaffer, SHRM-SCP, SPHR
Chief Human Resources Officer
Philadelphia, PA
roz.schaffer@rhd.org------------------------------