We haven't used a mover in years, and the last time we did they only moved furniture.
The best advice I can give is to have the movers move things like furniture and appliances, and move everything else like dishes, electronics, valuables, breakable items and clothing yourself. If need be, I suggest renting a small (16') box truck for your smaller items because its a hell of a lot easier and faster moving boxes on a dolly with a lift gate.