Negotiating pay when I have been out of work (update)

A recruiter asked for my salary expectations on a first call as I look for work as a social media manager. I do not usually post, so bear with me. I looked up ranges in Memphis and they vary a lot. How do you research fairly?

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.