I've had all four.
Birds, to be cared for correctly, require a lot of (expensive) equipment and attention. Birds aren't meant to live inside and to have an inside bird healthy and happy you need to be very knowledgable about birds. Most birds are very expensive too. Many of the larger, more beautiful breeds are 500+$. You cannot "play" with a bird. It is literally more like a living ornament. You cannot handle most birds (they bite or claw you. they have to be very used to you to be handled most times. especially the smaller more affordable birds) And you said you have two cats. These will most likely torment the bird. A very very bad idea. The bird will not be healthy or happy. I say no bird.
Bunnies are similar to birds. They require a lot of care and equipment to get started, and they are messy and sometimes very mean. I had a bunny for about two days when my uncle let his sleep at my house. It was truly miserable for all involved parties. The bunny pooped EVERYWHERE and scratched and bit me. It was not happy and neither was I. It made a lot of noise, and again, I think your two cats will torment it. I say no bunny.
Dogs are good, but they (especially puppies) require constant monitoring and care. They will chew everything, have to go on walks multiple times a day, ruin parts of the home if not closely watched, etc. And with your two cats that you already have, puppies can really rile up the existing pecking order of pets. The dogs and cats will probably fight A LOT and unlike another kitten, a puppy could really hurt a cat without meaning to. Typically kids promise to do all this stuff, but they really can't, and the burden ends up on the parents to raise the puppy. I'd lean against a puppy.
You already have two cats, so another should fit in fine. Kittens are easy to raise, and you already have all the equipment like litter boxes and everything. I vote for a cat.
You have to consider what you already have and what you are capable of. Pets aren't just because you "want" something. You have to be ready to care for them. They're living breathing animals with feelings and wants and needs. Whatever you pick, take the decision very seriously and really look at what you're able to give to an animal not only with your physical capablilties but with your home and economic status. getting a kitten spayed/neutered can cost about 100 dollars, along with their feline aids and lukemia vacation even a kitten can be very expensive. Your puppy would need similar treatments too. Think about vet costs (and even things like birds and bunnies need vet visits too, but they'll probably be more expensive because you'll have to go to a specialist) and think about where tehse pets will go when you go on vacation. Who will be taking care of them? Will these pets go to college with you? This is a very serious decision that shouldn't be taken lightly at all.