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Old Major is chosen because he is the wisest of the pigs. His initial setting forth of the philosophy that becomes the founding philosophy of Animal Farm should come from someone who has the wisdom that comes from being "old" and having lived long.
Snowball - the white pig seems to be pure in heart, hoping for that which is best for the pigs. He is the symbol of Leon Trotsky, who in most pictures that we see of him today, has white hair. It seems fitting that he would be white.
Napoleon - this name, reminiscient of the French dictator, reminds us that people who go on to gain absolute power, become focused on their own needs and desires. Like Napoleon, he becomes an autocratic ruler who thinks only of how he wants to rule and what he wants to be done.
Squealer - the pig who is the propaganda master has the perfect name to describe both the sound he makes and the way in which he "squeals" to the animals about what they must do if they are to fit in with the philosophy that Napoleon wants to thrust on the animals.