Basically I suggest rabies vaccine and FVRCP (may also be called HCP, FCP) vaccine for all cats, and to keep those boostered as needed.
If your cat is over 16 weeks with no vaccine history, I would suggest 1 FVRCP and in 3-4 weeks, another FVRCP vaccine which will then be good for a year. But some vets will just do 1 for an adult with no history. FVRCP protects against Feline Viral Rhinotracheitis (Herpes infection), Calici Virus (URI that is hard to treat because the infection causes mouth ulcers making cats not eat, and the best antibiotics for it can't be given on empty stomach), and Panleukopenia (AKA Feline Distemper, and the father virus of Canine Parvovirus). All of these diseases are highly contagious and deadly.
If the cat is under 1 year old, I highly suggest FeLV vaccine regardless of lifestyle. FeLV is feline leukemia, there is no cure, it is terminal, and it is transmissible through contact with saliva. After that initial vaccine, I usually only suggest getting the FeLV vaccine again if the cat goes outdoors, you have cats in your house that may be FeLV+ (like fostering kittens/cats), or maybe you work in an animal shelter/veterinary medicine type of setting.
There is an FIV vaccine - FIV is basically Feline AIDS but it is transmitted via saliva to blood, so mostly fighting and mating. It is also terminal and no cure. It is incredibly common in intact male outdoor cats, because they fight a lot. However, vets usually DO NOT recommend the FIV vaccine due to crappy efficiency and side effects. I wouldn't recommend it, either.
Over-vaccination doesn't generally happen as much with cats because we don't care about cats enough. This tends to happen more with canines and the DHPP/Lepto combo vaccine.
Nowadays vets will kinda hold your hand through all this and show you what they offer. Remember boosters actually do matter, your animal's immune system will forget it after a while. Let me know if you have any questions though! Good luck with your kitty
