How do I figure out a proposed budget for a book?

It sounds as though you may be dealing with a “vanity” publishing house, which is one who will publishing anything for anyone, as long as they get their money, “up front.” You need to be very wary of those businesses, because even though some of them are perfectly legitimate, many others are not.

There’s an article here that might address your budgetary questions:

http://www.fonerbooks.com/paper.htm

I suggest that any company offering to publish a book for you, be investigated very thoroughly by you, and one place you can do that (if you are in the USA) is here:

http://www.bbb.org/

I wish you all good luck with your project and hope that it brings you the kind of success you are seeking.