Fieldwork will definitely get your foot in the door. In my case, I got my first job at a snf through an agency. I was brought on to cover for 5 days but they were impressed with me and wanted to keep me on full time. I stayed full time for a month and a half because I had a hospital job lined up the following month. I'm still there every other Sunday.
I got my hospital job from faxing my resume directly to the rehab dept and following up with the director on the phone several weeks later. She didn't have any openings but interviewed me anyways. Sure enough, two weeks later, someone was going on medical leave.