You might want to build this based on some other fields as a start with over-rides for manually moving things around.
If your ordering is truly arbitrary, then you can do it all with just one field. I call mine "Arbitrary Order". That's hard to spell and weird, so you might want to use something simple like "order", or "shelf" or something.
Once you have established some kind of order, inserting in between two, (like between 7 and 8 ) is actually pretty easy: Just multiply all of them by 10 first. So 7 becomes 70. Position 8 becomes 80. Then you have 9 slots in between 70 and 80 to work with. It's easy to do in one shot:
Highlight all albums, open the tag action window; find your Order field and type:
=math([Order Field Name Here] * 10)
Press enter and they will all multiply by 10.
In practice, this becomes kind of unwieldy though, as typing numbers into fields isn't nearly as easy as dragging things around. This is why I suggested that, if your scheme has some logic to it, that you replicate that logic using fields.
As a weird example: I knew a guy a long time ago with a GIANT collection of movie soundtracks. He organized them by:
Alphabetical Movie Genre (like Western, Action, etc)
Year of Movie
Alphabetical Movie title
All neatly on a bunch of shelves.
You could replicate this digitally with a few fields and be off and running. One of your fields could be a numeric field so you could tweak things around.
Good luck.
Brian.