It is best to avoid any exposed asbestos. If you must be around damaged asbestos siding, make sure to wear a protective face mask that is approved for asbestos use.
It may be possible to encapsulate asbestos siding behind a layer of new siding, thereby preventing asbestos from becoming airborne.
Generally speaking, asbestos siding is safe to be around provided that it has not been damaged, and has not begun to decay due to age. Removing the material can cost thousands of dollars, as asbestos removal specialists must act in accordance with state and federal asbestos regs
You want to go with Fiber Cement siding available from either Home Depot or Lowes.
Avoid asbestos siding.
Of course since you are in New Jersey, once you remove the Original siding you may want to
Put new insulation unless of course you are putting the new siding on top of present exterior.