Or should I cut all of it out and ha e furnace installed with duct work?  

There is forced hot air in the house now, so the duct work is there.

Best thing that I have done is to charge a monthly pet fee and then put in lots on language in the lease stating that they have to have the ductwork and any carpets professionally cleaned at the end of the lease showing a receipt from a 3rd party explaining the next tenant may be allergic to pets.

So far we have replaced the ductwork and have had some closets built in. 

Back in those days asbestos was barely new to the market and was used for many things such as siding, plaster walls, insulation, duct work and even shingles.

Brush up on building code requirements: in basements you're looking for egress windows that are 5.7 sq feet or more openable (3ft by 3ft casement style windows work best), and ceiling heights 6ft 8 inches or greater (as little as 6 ft 4 inches is ok under ductwork and beams though)Sounds like your basement would be a home-run to generate some extra rental income - Happy to talk through the details of that strategy with you, just shoot me a DM! 

Brush up on building code requirements: in basements you're looking for egress windows that are 5.7 sq feet or more openable (3ft by 3ft casement style windows work best), and ceiling heights 6ft 8 inches or greater (as little as 6 ft 4 inches is ok under ductwork and beams though)2.

It's a 40 year old property, so the duct work, electrical, plumbing is outdated and weird, and I'll have to make the windows larger to be up to code for a bedroom -including cutting through the concrete and digging bigger window wells. 

You might wanna check how the ductwork for the bathfan was done up in the attic.

The only things we (he approved) hired out were the new roof, new hvac and ductwork, and new septic system.