Since you asked only about varmints and not deer or elk or anything else I am going to have to say the .223 Remington. I have taken prairie dogs with it out to 500 yards (700 yards with the AI version), a few badgers and thousands and thousands of ground squirrels.
Lot of cheap brass and surplus ammo, accurate, a whole bunch of bullets and load information and being a NATO round for the last 50 years means that brass will around forever.
Might not be the best choice for everyone, but if the only varmint caliber made was the .223 Remington I would be OK with that.