Interestingly, the current job only gave me ONE week to think about it. As a side note, universities will often use this as a tool to put pressure on you to accept (especially if they think that you are a good catch). You also have to understand that some times departments are competing for these positions , real estate (lab/office) space, etc. within the university; so the Department Head's point of view is that the longer he cannot bring you, the more likely it is that he will lose this position to someone else and end up with nothing. So they too have time constraints. In any case, 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.
But what I really wanted to tell you here is what you should and should not negotiate. The answer is easy:
You SHOULD negotiate your start-up package:
MONEY - this is the life blood of your lab, so obviously you want to ask for a lot, but at the same time you don't want to be unreasonable. also, for budget reasons they can break it up into two or three years (ie, you have to spend a certain amount by the end of that year, or it burns up!). This is both good (because it makes you hurry) and bad (because you might not want to spend all of your money according to the imposed time line) ... well, there is no such thing as "can't", but it is better to get what you want into your offer letter, because it is effectively a contract and cannot be disputed.
STUDENT YEARS - several words of advice here. This is typically discussed in terms of student years... say 2 students for 2 years makes 4 student years... what happens after that? Well, you are supposed to support them from all those grants that you'll be bringing in :) And what happens if you don't bring in any money? Do these people just starve on the street or go work in the 7-11? No, not really. The "secret" is that the university will budget their support through the end of their PhD. So don't stress out too much :) Also, the department will want you to take on the students who have already been accepted... well, chances are that by the time you get there, all the best ones will have been taken. So, you should try to recruit someone external on your own.
EQUIPMENT - I didn't get any, but I've seen other professors get things like biohoods, water filtration systems and things like that installed in their labs as a part of their start-up. The thing is that 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 - In line with what I said before, it is common for the university to charge you per hour for access to shared facilities, So you can negotiate one or two years of free access, for example if you need the microfabrication facility or something like that. Or, 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. The last thing anyone wants is for you to get stuck and not be able to do your work.
TEACHING LOAD - Well, I've heard 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, lets be honest, teaching is the most stable income that pays the professors' salaries (while research grants are very stochastic). Luckily, universities should be 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. Also, most likely they will allow you take one semester off from teaching to build your lab (this is standard). And most people (myself included) would probably prefer take the first semester off. But while this makes sense in theory, in practice 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. Therefore, it is my recommendation that you take the second semester off. Oh, and 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!
Update: Avoid teaching graduate core courses, at all cost. Firstly, undergrad courses are much simpler in terms of 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 (i.e., 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.
So, this brings us to things that you should NOT negotiate... And again, the answer is easy: you should not negotiate your salary. Because, after all, we are scientists, and we are not supposed to be doing this for the money (and the money you will be offered will most likely provide you with a comfortable living) :)