I've found the following to be the quickest way to allow specifying item order regardless of list size:
1) If user wants to set the order of list/grid items, they click a "Reorder" button.
2) This opens the reordering dialog which can be used with any list or grid.
3) In the dialog, all of the items are shown in their current order in a list on the left. There is an empty list on the right.
4) The user clicks the items in the left list in the desired order. When an item is clicked, it is removed from the left list and placed in the right list in the next position. In a worst case reordering where every item needs a new order, this allows ordering a list of N items with N clicks.
5) The user can then apply the new order or cancel. Applying the order results in the "display order" field in the data being set to the final order of the items in the right list. You can decide if the "Apply" button is only enabled when the left list is empty.
6) Also available in the ordering dialog are the following controls:
a) A button to move all of the items from the left list to the right list maintaining whatever order they are in
b) A button to start over by reloading the left list in its original order and clearing the right list.
c) A button to sort the right list alphabetically (or by date or numerically depending on what the key field is)
d) Drag and drop capability in the right list to manually drag items into order.
e) An index number column in the right list which, if edited, moves the item to that position.
This provides the best of all worlds. If you have a huge list where only a few items need to be moved, move all items over, then drag the few items where desired or enter the desired index. If you have a small-ish list that needs to be completely reordered, just click the items in the desired order. And so on.
I've used this approach for many years and it has been very effective.