If you get offer, congratulations!
Roman says "Interestingly, my current job only gave me one week to think about it. I went back for another visit (at my own expense), and negotiated an extra week. I was honest with the department head that I had an interview coming up with another university. He was understanding and gave the extra week. Anyways, the point is that you are now in the position to dictate things, because the ball is in your court."
You should also understand the mechanics of this business. Some times departments are guaranteed a position, while other times they are competing for them. So if you don't accept their offer, they could lose the position to another department.
Here is what you should (or not) negotiate:
Money: This is the life blood of your lab, so ask for a lot, but don't be unreasonable. For budget reasons, they can break it up into 2-3 years.
Student Years: This is typically discussed in terms of student years: 2 students for 2 years makes 4 student years. What happens after that? You are supposed to support them from all those grants that you'll be bringing in. What happens if you don't bring in any money? The "secret" is that the university will budget their support through the end of their PhD. The department will want you to take on the students who have already been accepted. Although chances are that by the time you get there, all the best ones will have been taken. You should try to recruit someone external on your own.
Equipment: The department and the physical plant (who work together to set you up) get a fund from the university to renovate your lab, and get it customized to your needs. Installing outlets and things like that all cost money, and the internal university entities actually charge each other for that to happen. Things that simple to you, like installing a 220V device can cost you almost more than the equipment itself if your lab only has 110V.
Access to Shared Facilities: It is common for the university to charge you per hour for access to shared facilities but you can negotiate one or two years of free access. Maybe your school doesn't have the facility you need, but the one across the street does; you need to communicate all this to the department head so he will understand your needs and help you meet them.
Teaching Load: We have heard that you should ask for this to be put on your offer letter but at the same time universities aren't terribly flexible about this because teaching is the most stable income that pays the professors' salaries. Universities should have some kind of structure to help you ease into the position. For example, during the first 2-3 years your teaching load would be reduced, and then it would go up to normal levels. Most likely they will allow you take one semester off from teaching to build your lab (this is standard). You may not get access to the lab until the second semester (there can be politics involved with freeing up the space) so the opportunity would be wasted. It is therefore our recommendation that you take the second semester off. Put the lab number on your offer letter - it is always good to ensure that you will get what you were initially promised. Remember, the offer letter is a contract!
Try to avoid teaching graduate core courses. Firstly, undergrad courses are much simpler in terms of the material. Secondly, grad core courses have a lot of MS students. The difference in the number of students between core and non-core courses can be as much as ten times more for the former (e.g., 50 students for a core course vs 5 for a non-core). Moreover, in the non-core courses, you will be teaching mostly PhD students. They are much easier to work with.
The optimal scenario is if you are allowed to develop your own course, which you can then use to train students for research in your lab.
Your Salary: After all we are scientists and we are not supposed to be doing this for the money.