The best method to avoid germs and odors is to use laundry hampers with features like several compartments, detachable liners, and waterproof construction.
A decent-sized hamper or basket is usually preferable because you'll have to handle it unless it's on casters. However, your space ultimately dictates the size of the hamper.
The amount of washing your household does and the size of your home will determine this. A large family may want many baskets or one for each member, but one large hamper should be enough for two people.