Congrats and good luck
Recently had a complete pack and move for a 5 bed house 200 miles and unload into a storage lockup £2,500 - lot of built in furniture and the beds were left behind, still a lot of boxes
Our move cost £1,500 4 bed house plus garage and shed but that was nearly 7 years ago
EDIT: It really does depend how much stuff you have - they come round and do estimates free though