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

I do not know whether to give a range or ask for theirs. I have been trying to stay organised about it. I do not want to price myself out. How do you research fairly?

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

Benefits matter too. A slightly lower rate with better coverage was better for me.