About 8-10 weeks is a good age, and it's not just tons of shots one day and done, it's a series of them over 3-6 months or so. Rabies, distemperment, deworming, snap test for kitty AIDS and cancers, etc. My husband and I spent about $340 total for appointments, shots, tests, and follow ups (this did not include neuter), but again, not all at once. Other vets are more expensive, so you have to do your shopping. Some vets offer kitten packages that you can pay all at once or pay off over time. These often included the price of the fixing, too. Really, it all works itself out to be the same in the end, no matter what you choose.
I'd stay away from "chain" vets, like Banfield. They are overpriced and will rip you off at a moments notice. Just look in your area.
Kitties and puppies are like kids: they are not cheap in the beginning, so you'd better have the funds and backup funds to keep your animal happy and healthy. Altogether, our kitten cost about $950 the first year; initial start up of toys, littler, food, kitty tree, etc., and all the vet care and neuter. Good luck.