This, from the tweets, generated a few thoughts:
Faculty negotiation: 1) Salary, 2) start-up package, 3)HR benefits, 4) Moving expense, 5) space for research 6) Teaching load, graduate student access and support, 7) promotion/tenure process, 8) IPR, 9) Parking/housing/child care and 10) Spouse/partner employment#SfN17
— Addictive Brain (@addictivebrain) November 11, 2017
Hmmm... I disagree with order, for sure. But the first thing to consider is what is the ballpark of the starting place from their side? If something is "close" to what you want/need, it may be a better strategy to set that aside and put your negotiating towards the things that are not. Thus if the lab space is close, but the salary not, don't argue for an extra 100 sqft, but for the extra $10K in salary.
Also keep in mind that a "final offer", the legal piece of paper won't be made until you and chair have reached an agreement about what the position is and it entails. Thus your negotiating can be delicate in balancing what you need vs. what the department can offer.
As for order: if you don't have what you need, in space or other resources, to be a success and publish, get funded, in short do your job as a scientist/professor, it doesn't matter how high the salary is right now. If the teaching load is so burdensome that you can't do research, and research is what gets you tenure, it doesn't matter what the salary is, or how much they give you for child care.
You are playing a long game now, and you need to think about what will carry you for the next six years. Which suggests one point to inquire about: how long can I keep the start-up (seed) money. Sometimes it needs to be spent in a window, and sometimes that window is a year or 3 years. That can be a problem if you haven't gotten funded by then.
Also, it is worth keeping in mind that there are some things your (soon-to-be) chair can't negotiate. Things like HR benefits are often determined well above the chair level, and sometimes at state universities they are set by the State Legislature. Ask about them, but don't get hung up. The same can be true of parking/housing/child care. Money is fungible: salary can go to parking, childcare, or moving. And $1000 now for moving (which may seem very important) is not worth as much as $500 more in salary, multiplied over 6 years, and including %age increases.
Teaching load is tricky. In this day and age, jobs are often defined by teaching needs: its where the money for the line comes from. Try and find that out during the interview. If they absolutely need someone to teach: A&P to pre-nursing students, or Intro ecology for a well-subscribed program, your trying to negotiate out of that teaching can result in a final offer not being made.
A good chair will let you know where she/he is flexible in the offers that can be made. What teaching can be delayed or traded? How are salaries set, and what is the range for this level of professorship (lots of public universities have set ranges)? What about space? What about renovating space? One likes to think everyone is negotiating in good faith, and that the chair wants you to come and doesn't want you pissed off. But remember to get it all in writing. The chair you negotiate with today may not be around tomorrow.