What should the startup package consist of at US (primarily) undergraduate institutions? What should one list in the startup funds if you are taking up a tenure-track position at a public undergraduate university in the US, mostly focused on teaching? I'm asking specifically for mathematics/applied mathematics/computational mathematics.
What do you think you really need in order to conduct your research program? Can you justify why you need these things in order to conduct the research?  How much of this is so important that you'd turn down the job offer if you didn't get it?   

Things that you might ask for include summer salary for yourself for a year or two, computer equipment (say $3K for a nice desktop computer up to $100K for a high performance computing cluster), funding to travel to conferences or money to pay undergraduate students to work on your research with you. 

At a regional comprehensive undergraduate only public institution, chances are that there isn't much money available for a startup package.  Based on my experience, I'd be surprised if you could negotiate for much more than a couple of months of summer salary, a few thousand for travel expenses and a few thousand for a desktop computer.  At an institution with a graduate program, you might also ask for support for a graduate student.   

In negotiating these things, you're likely to find that the chair of your department (or search committee members if the department chair is negotiating with you) can be helpful in telling you what others have received in the past and what the administration is likely to fund.  

Whatever you do ask for, be sure to ask politely and don't let it seem as though you won't accept the offer unless your wish is granted.  It's not unheard of for offers to be retracted in the face of startup package demands that are too high.  You should also give a budget with justification rather than negotiating for a simple dollar amount. 

The strategy of negotiating the salary and startup package verbally before a formal offer is quite common.  It is a smart negotiating tactic on the part of the institution since you have nothing to fall back on until they make a first written offer.  If you demand too much, they can simply move on to another candidate without ever making you a formal offer.  Another advantage of this strategy is that it forces you to make a decision quickly- you can't draw out the process with multiple rounds of offers and responses.