If you are installing a whole new system, most HVAC contractors will not touch asbestos insulated duct work, but some asbestos abatement contractors are also HVAC contractors. If you can find a HVAC contractor who can deal with any necessary asbestos abatement as part of the HVAC upgrade, this would be ideal.
As far as removal, your best option depends on whether the project requires replacement of all ducts, or just replacement of the central air handling unit with connections to existing ducts.
If the ductwork is to be replaced, old ducts can be left in place (no abatement), or removed in whole sections (wrap insulated pipe in plastic and remove in sections, with sections to be cut cleaned using glove bag removal). If the duct work is to be re-used, it is possible to remove asbestos insulation from the point that will be affected by the new connection. Note the old furnace may also have asbestos insulation (looks like mortar) on top.
The danger of removing asbestos depends on the methods used, and precautions taken by the contractor. Asbestos removal is not rocket science, but it requires some expertise, equipment and materials not readily available to most homeowners. Done properly, it poses minimal risks. Expense can be surprisingly reasonable. You are primarily paying for skilled labor and waste disposal. Explain a little more detail about the system and project (type of insulation, length and diameter of pipes, whether ducts will be re-used) and I may be able to make suggestions. Alternatively, get bids from contractors for abatement.