Get a minimum of three bids. Estimates for an average-sized job should be within a few hundred dollars. Be suspicious of anything that is substantially lower or double the price of the rest, and watch out for hidden fees, like charges for travel expenses. They could be signs of a home improvement scam. A good plumber will not nickel and dime you like this, and many of us will offer free estimates.
The word "plumber" dates from the Roman Empire. The Latin for lead is plumbum. Roman roofs used lead in conduits and drain pipes and some were also covered with lead, lead was also used for piping and for making baths. In medieval times anyone who worked with lead was referred to as a plumber as can be seen from an extract of workmen fixing a roof in Westminster Palace and were referred to as plumbers "To Gilbert de Westminster, plumber, working about the roof of the pantry of the little hall, covering it with lead, and about various defects in the roof of the little hall". Thus a person with expertise in working with lead was first known as a Plumbarius which was later shortened to plumber.