Two dogs definitely cost more money but how much more also depends on you. Will you buy a lot of new toys for the puppy, go to puppy classes and so on. When I got my second dog the expenses were pretty high in the beginning (as you said, the vet visits, shots and so on) and now it's a little better. But still, two dogs eat more, need more treats, get sick sometimes.... It is a lot of money but to me it's worth it!
Good luck with your new pup!