There is no cheapest airline, it depends when you want to travel. It also depends on the season on when you want to fly out because if it is near a holiday or vacation time then prices tend to be high. So I advice you to check online prices of tickets and monitor it for at least a week
Allegiant Air is a very economical airline. But it doesn't fly to and from all cities. They have non-stop flights which are great. The next best bet would be Southwest Airlines, and they do not charge for baggage.