If it's at all research-related, you likely should not be paying for the item with your own funds. That includes software, textbooks, laser pointers, society memberships, conference travel, and so on. When in doubt, ask.
To make purchases, let me know what you wish to buy. I will, in return, give you a chartstring (a sequence of letters and numbers) that you can use to make the purchase. With this, you can e-mail my faculty assistant, Kaleigh Lane (kaleigh.lane@princeton.edu), to make the purchase. Please CC me on the e-mail.
All relevant university policies apply for any purchases you make. In general, all physical items you purchase with research funds should, by default, be considered to be "on loan" to you while you're in the group. That said, in general, you will be allowed to keep most personal use items (e.g. laptops) upon graduation when possible.
Using software without the proper license for research-related activities is strictly forbidden. If you need something, just ask! Don't worry about the price.