I personally do not like the idea of pets in the classroom at all. I think no matter how "simple", small, or quiet the animal, it's not going to be an ideal setting for a pet. Additionally, if a child develops an allergy, gets bitten, or becomes anxious, what happens to the pet? Whether it's a bird or a hamster or a turtle, you need to accept the very real liability that curious children can and will get bitten. As an adult who gets bitten, I can say a) it hurts, and b) it sucks. I think fish would be an okay pet as long as you were able to buy and maintain a proper aquarium, bearing in mind that even common goldfish are capable of living ten years.
What is the purpose of wanting a pet? If it's going to be based on teaching children gentle handling, responsibility, and caregiving, plants are a better, safer, cleaner, and easier resident for a classroom. If you want the children to be able to develop a bond or have a classroom mascot, a stuffed animal is easier and safer too. The bonus of a stuffed animal is that the kids can take turns taking it home for the weekend and journaling the adventures they had with it and such. I think this was one of my favourite gradeschool activities.