Checking for criminal records is different from “skip tracing,” though some of the records do overlap (e.g. if the person you are tracing happens to be in the criminal justice system). Here’s a terrific Skip Tracing guide by the King County Law Librarians for Washington State residents. It can be adapted for Oregon.
Skip tracing isn’t a fast, cheap, or easy thing to do, just as criminal background checking isn’t. But you can do a lot of it yourself and then hire a professional to do the tricky bits that require specialized or expensive databases or particular expertise.
I’ll save Employment Background Checks for another day.