They asked my salary range, what should I say? (update)

I have been out of work for 10 weeks and feel pressure to accept less. There are 11 people counting on me, so I am trying to be careful. I do not want to price myself out. How do you research fairly?

Keep everything in writing and save the confirmation numbers. It made the follow-up calls so much easier.

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