How to save a particular, mutable “order” into a database

Question

Suppose I have some objects, and I want the user to be able to reorder them in any way they wish, say, by dragging them around. So I\'d have

• Cheese
• Muffin

Answer 1

Looking at Tony Andrew's and Mark's answers in particular, it seems I really have only two alternatives:

• Saving a 'next' value, making the objects behave like a linked list (see Mark's answer)
  With this, changing the order is cheap, but I'd have to retrieve the items and then sort them by their 'next' value, which is expensive
• Saving an 'order' value (see Tony Andrew's answer)
  This makes retrieving cheap but saving a new order potentially expensive, because in the worst case, I'd have to change all the order values. cletus points out that one could use a large number in the form of 2^n for the order multiplier.

Meta: All of these answers are good and correct, which one should I choose as correct?