If you’re just doing boxes (or even small pieces of furniture), UPS or USPS will be a much better deal than movers. Case in point: my brother was getting rid of an end table (heavy, wooden) that had been my grandmother’s, so I wanted it to stay in the family and offered to take it. We live about 1000 miles apart. A mover would have been completely unaffordable (like $1000.00). UPS boxed and shipped it for about $175.00. For misc. boxes, USPS has a weight limit of 75 lbs. and pretty reasonable prices, relatively speaking.
Of course, it depends on how much stuff you’d want moved or shipped.