I don't do my own animals because I'm not comfortable with it, but I know that cats need rabies and Feline Leukemia shots once a year. They do make a rabies shot that is good for three years now and my cat has had that one. I think that's the only other one, but I would call a vet's office just to see what is required by your local state laws.
Yep, I've done my own pets for years. I usually go to the feedstore (or tractor supply) and get the one that covers the most stuff. Cats can be tricky because they have such tough skin, be sure to jab pretty good when you do it. Sounds harsh, but it's easier than trying to do it 2-3 times. Those kitties get peeved when you do that!!
I always keep the container the vaccine came in (either box or bag) and write the animals name and date on it and keep it in a file. It helps to remember when it was done. Also is proof it was given if ever needed. Rabies are always done by my vet.