No one airline consistently offers "cheap" air fares. Ticket prices vary with the season and even the time of day. Decide what your budget is and then register at one of the discount travel sites (Expedia, Travelocity, Obritz, etc.) and see what the going rate is. The more flexible your travel schedule, the better prices you can usually nail down. Most major airlines allow you to check two bags within the weight restriction. There is no airline that allows unlimited checked or carry on baggage.