My tax ID number would just be my Social Security number and I don't especially want to give that out.
Many years ago when my attorney found out I was doing business under my own name she went ballistic on me. You need to form a corporation, get a TIN, and make sure you do all your business through the corporation. Otherwise you're potentially putting yourself and all your personal assets at risk.
Obviously you should talk to your lawyer about your own unique situation as WebmasterWorld is not the right place to get legal advice. :)
On a side note, verify this situation is legit. As others have mentioned word about good vendors spreads quickly through the academic community. Just like many of us have our own niche websites the same is true for teachers and professors. No doubt they share information about who's good and whom to stay away from.
Good luck and I hope things work out well for you! :)