This varies enormously between universities (see Suresh and JeffE's comments, for example). At some schools, having a soft-money position means very little. They are basically just saying you are allowed to use their name to apply for grants, and to pay for things like office space using grant funding (including overhead). In such a case, there may not be much to negotiate over, since they intend to make a profit from you, not spend money on you. You could ask for adjunct status, and the salary requested in grant applications might be determined by the university, but most of your other issues (space, travel, equipment, assistants, etc.) would be handled in the course of dealing with individual grant applications, rather than specified in advance. The key would be getting large enough grants to pay for them.
At other schools, particularly in medical fields but sometimes elsewhere too, being a research professor can be very serious: you may be a full faculty member, attending and voting in faculty meetings, with the possibility of tenure. Of course, tenure on a soft-money position doesn't mean much, since the university never gives you a salary. If you don't get grants, you don't get paid. But it does mean that as long as you get grants, the university cannot get rid of you. (This can be a genuine issue in some soft-money positions. If the regular faculty don't think you meet their usual standards, then the department chair may eventually be tempted to push you to leave, so you do not seem like a permanent fixture and start to affect the department's reputation too much, or to make your lower status clear in other ways. A tenured soft-money position is a real indication that the department values you, even if they aren't paying for you.)
How you should negotiate really depends on the sort of position. It can't hurt to ask how anything you care about works, and the worst case scenario is being told it's not negotiable.
One thing I'd avoid bringing up is authorship issues. This is something that should be discussed at the level of individual projects, and bringing it up here may make people worry that you are asking for something inappropriate (like guaranteed authorship just for providing funding), even if you have nothing like that in mind. If you do discuss it, you should make it very clear that you are just making sure everyone is on the same page, rather than trying to negotiate special rules that would be guaranteed to apply to your job.
One thing I'd add is grace periods between grants. If all goes well, you'll arrange overlapping funding, so you will not have a period with no active funding. However, it might well happen if you aren't lucky, so you should discuss how that would work. For example, if you had a gap between grants, would they immediately take away your office when the first grant expired? If you reached a state in which all your grant proposals had been rejected, with no pending applications, then would that be the end of your job? Or would they allow you some period of time to continue making applications?