Negotiating pay when I have been out of work - 20 weeks in

I do not know whether to give a range or ask for theirs. I have read a lot of threads here and could not find my exact situation. 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.

Keep everything in writing and save the confirmation numbers. It saved me later.