Moving companies

I'm moving from Md to Fl in June. Looking for a mover and getting quotes is a chore. Question - how important would it be to you that the mover be a member of the Better Business Bureau? For example, the Bekins agent I'm awaiting an estimate from is not a member of the BBB. Should that matter?

BTW - getting the Dart shipped the end of Apr for $650 with delivery to my brother in law's May 3rd. Can't afford to drive it with premium gas and 8mpg!!