Negotiating pay when I have been out of work - any advice?

A recruiter asked for my salary expectations on a first call as I look for work as a project coordinator. There are 12 people counting on me, so I am trying to be careful. I looked up ranges in Memphis and they vary a lot. How do you research fairly?

Check several sources for pay in Memphis, then pick a range where the low end is one you can live with.

I gave a range based on local postings and said I was flexible depending on the whole package. They did not push back.