Unfinished basement is open to vented crawlspace, what should we do to finish?
If the furnace is not one with an open flame, I would seal up / insulate the hole around the air duct that goes to the crawlspace side, then finish off the basement side as desired.

If the furnace has a flame, I'm not sure what you will need for combustible air and safety reasons.  You definitely need a carbon monoxide detector on the basement side if there is combustion.