A vertical air handler and a horizontal air handler is the exact same piece of equipment. They are made to be up-flow/horizontal. If you want to move it up to gain floor space, that shouldn't be a problem unless there isn't room.
Make sure the air handler cabinet is insulated on any price quote you get.
Personally, I would never use wood in any duct system. That wood box should be made of sheet metal and it should be insulated inside or out.
Not sure if your "moisture issues" are condensate removal related or duct/cabinet sweating. Either way a quality contractor should address those at the time of installation. Mention it.
A quality contractor will run a manual J heat load calculation to determine your needed capacity and not just replace your current size. If changes are being made in capacity, duct changes will also have to be made.