The one advantage of using something like anyvan or Shipley is that you can send a photo and you don't have to provide accurate weights. With some others if your weights/dimensions are incorrect you may be charged extra.
Not that it helps with your courier choice, but I remember when my 10 gun Buffalo safe was delivered. I had gone for the upgraded version, 3mm walls instead of 2mm and a 6mm door instead of 3mm so rather heavy! The delivery driver raised the tail lift to shoulder height and was just about to throw it on his shoulder. He miss read the kg thinking it was pounds lucky I stopped him as it was 124kg not the 124lbs he was expecting!