I think the first set of shots is the most crucial. There are many diseases such as panleukopenia that can be virtually eliminated by appropriately vaccinating. Even though your cat is indoor only, what if it escapes? Or there could be a natural disaster that may let your cat out of the house. Mice, fleas, and other insects can cause diseases. Therefore if you get a new kitten/cat I feel it is important to make sure they have at least their first series of shots. If you travel or even have your cat groomed a rabies shot may be a necessity.

Also even though some have had a bad experience with a vet, there are vets out there that are wonderful. I would never hesitate to get my cat to one if I had any question or felt something was wrong.