Beware of the cheapest moving company. Basically you are buying a service and the less you pay the less you will get. Cheap movers will usually cut corners on things like packing and supplies. They...
Uhaul is probably the cheapest, but be careful when renting from them since many of their local offices are not reliable (check their BBB record to see why).Budget or Penske would be a more reliable...
Most major moving companies do sell boxes to the general public. Another option is to check out Craigslist for free moving boxes or your local grocery store.