All kittens should receive the feline respiratory vaccine, abbreviated by vets as “FVRCP”.
That stands for Feline Viral Rhinotracheitis, Calicivirus, and Panleukopenia. All 3 cause upper respiratory signs in cats, which can be mild to life-threatening.
In order to be fully protected kittens need a series of 3 vaccinations, given 3 - 4 weeks apart. Most veterinarians recommend starting these vaccines at 8 weeks, then repeating at 12 and 16 weeks. That schedule might be slightly altered if the kitten is already ill since it’s widely believed that vaccinations aren’t as effective at inducing an adequate immune response in an ill animal.
All kittens need a rabies vaccine. Most veterinarians recommend giving this vaccination at 16 weeks of age.
Depending on where the kitten will live, but particularly whether it will go outdoors, the veterinarian may recommend vaccinating against feline leukaemia, which is a serious and life-threatening viral disease that’s contagious. There’s no cure for feline leukaemia, but if a cat is going to live indoors its chances of contracting the disease is zero, so this vaccine isn’t typically given to indoor cats.