factory air conditioning box w/ controls

Much easier to go with an under-dash unit, but they do take up a LOT of space in an early A. Any front-seat passengers will hate it.

Next easiest would probably be the Vintage Air unit. It's been done before in a 64 - basically the same dash and engine bay as your 63 model - and looks like it doesn't need any major changes (at least nothing that can't be done in areasonably well-equipped home garage) - http://www.slantsix.org/articles/vintage-air/Vintage_Air.htm. I think the hardest part would be making the brackets to hold the evaporator unit.

AFAIK, you're in uncharted territory with the later factory unit - if you do decide to go that way, pull out your existing heater, then take a lot of measurements inside the dash - don't forget that the cowl plenum and the windscreen wiper mechanism take up a pretty big chunk of the available space back there. If you need to cut or weld anything, or you need to farm out any of the work, it could easily end up costing more than the Vintage Air unit.