I think it is important to review what you want: position, hours, location, size of facility, and to think about the pros and cons of what you have like about what you have done. That said, start your research.
If you know where you want to go, and better yet, what area, how lucky you are. You can find out, from the facility, who they use. The more unknowns you are dealing with the more complicated your decision and research. I am sure you know to keep good notes, make a list, etc...
There are the big companies talked about here. Try to look into the smaller companies that go unnoticed. I have heard of, and am currently attempting to subcontract with a smaller Agency that really is working on my behalf. Their billable is lower so I can, theoretically, get more extra shifts. The down side is, processing takes longer and the "owner" is pulling shifts and not available 24/7.
We are the commodity, we just need to know what we want, and be willing to wait it out to get what we want. Interview, take notes, know the billable
Thank you for your kind words It is appreciated.