On an oil furnace, the technician typically replaces the nozzle and filters, checks the electrodes and pump pressure, and takes combustion readings. On a gas furnace, the focus is ignition, flame sensing, gas pressure, and the vent. Either way, ask for a carbon monoxide check.
For a replacement, the contractor applies online and must have the permit card before removing the old furnace. If the job includes an oil burner or tank, the installer then has 7 days after finishing to call the fire department for its inspection. Ask who will be home to let the inspector in.
Newer homes usually have open basements and standard stairways, which makes equipment easier to move. Attic duct work is the exception, so mention any finished attic space or tight access.