In my opinion, the best option would be to insulate the floor (ground) of the crawlspace and the foundation walls essentially making this area conditioned space.
The best insulation for this project would be 2-pound, closed-cell spray-applied foam insulation. Closed-cell foam insulation is a vapor barrier so it would be fine sprayed directly onto the foundation walls.
- Your code jurisdiction may require spray-applied foam to be Class I (flame resistant) or covered with an approve fire rated coating (also spray applied).
- The same material can be used to seal and insulate the soil but it would need to be covered with a puncture proof covering to allow for traffic in the crawl space for future repairs.
This option keeps the furnace and ductwork within the thermal envelope of the home so duct leakage, soil gases and moisture are not introduced into the home via zone depressurization.
You didn't say much about the configuration of your crawlspace (size or condition) so I made the above recommendation as a blanket "best case" scenario from a performance perspective.
- Your insulation contractor may have other (sheet foam) options that may be less expensive and perform nearly as well.
- I would be hesitant to use any insulation that is air permeable behind a vapor barrier because vapor barriers fail and you don't want to trap moisture in the insulation making it less effective and a potential source of mold growth.
Good luck with your project.