We have discussed various aspects of what you need to do to secure a tenure-track job offer: CV, job talk, interviewing, etc. You've done well with all of this stuff, and you have one or more offers. Now let's discuss how to negotiate the particulars of the offer, to best maximize your chances of ultimate success.
In the interests of honest disclosure, I want to start with the story of my own "negotiation", so you can decide whether to even listen to a single fucking thing I have to say on this topic.
Dept Chair: Hello, PP? This is Dept Chair. I am calling to tell you that we have decided to make you an offer for the faculty position.
PP: I'll take it.
Dept Chair: Umm, how about if I tell you a little bit about the offer?
Dept Chair: Well, we will give you suitable lab space, a suitable start-up budget, and...
PP: I'll take it.
Dept Chair: Umm, how about we send you a draft formal offer letter, and you consider it for a few days, call me if you have any questions or concerns, and then we can generate a final version for signing.
PP received the letter, barely looked at it, signed it, and sent it back.
Fortunately, Dept Chair is an extremely fair person, and she provided an offer with ample start-up funds, protection from teaching and admin stuff for a year, and excellent renovated lab space. If she had not been operating from a mindset of "we need to give PP the resources to succeed", I would have been in big trouble.
Bottom line: I didn't even attempt to negotiate. However, there is a very important broad lesson to take from my story. If at any time during whatever negotiating you do engage in, you begin to get the sense that the chair (or whomever you are negotiating with) is trying to drive the hardest possible bargain, without any consideration of what you would actually need to successfully get your lab off the ground and reach externally funded self-sufficiency, that is a very, very, very bad sign.
The reason my chair provided me with a more than ample start-up package is because she was operating from a position of enlightened self-interest--my ultimate success or failure inures to her benefit or detriment as a chair--and commanded enough resources to satisfy what she perceived as my needs.
This highlights what should be your goal in negotiating the job offer: making sure that the person on the other side of the table is absolutely clear on what you need. If you absolutely require an expensive piece of equipment, you need to make sure that the chair is aware of this. No one will fault you for vigorously advocating for your needs in terms of your research program. In fact, it will demonstrate maturity and persistence that you know what you need, and are willing to engage in a possibly uncomfortable negotiation to obtain it. And this includes things like "protected time" in your first year or so, away from teaching and administrative duties, start-up budget, specialized equipment, space, and access to core facilities.
One thing that is key to recognize, however, is that this negotiation is only the beginning of your relationship with the chair (and the other senior faculty in your department, and maybe even deans, who will surely hear about the negotiation if there is anything out-of-the-ordinary about it). If you leave those people with a bad feeling about your motivations, or your ability/willingness to be a "team player", you are setting yourself up for a rocky relationship going forward. And these are people whose opinions of you will be extremely important as your career progresses.
As I said, there is nothing wrong--in fact everything right--about advocating for what you truly need to get your lab started and ultimately self-sufficient. But there are things that can end up self-defeating. One of the most significant is your own salary.
If the initial salary offer is reasonably consistent with that of similar insititutions for similar positions, then it is a really bad idea to try negotiate the salary upwards. First, it is extremely unlikely that the salary will go up very much for an entry-level tenure-track position. Second, you will suggest to your future colleagues that you are viewing this as a "job" and not a "calling". (I am not opining on whether it is a good thing that people concern themselves with this distinction. The fact is that they do.)
So, the bottom line: (1) Negotiate in good faith for what you genuinely need, and not just to maximize the size of the package. (2) Make it clear that your only consideration is the success of your research program, and not your personal enrichment and/or aggrandizement. (3) If you get the impression that the chair is not approaching the negotiation from the standpoint of wanting to, and being able to, provide you with everything you will need to reach escape velocity, be very wary of taking that position.