On an oil system, expect the technician to check the fuel supply, filter, nozzle, and ignition before condemning anything bigger. On gas, they will look at the igniter, flame sensor, venting, and pressure switch. Either way, ask them to explain what failed and whether the fix is temporary.
A straight repair usually needs no permit, but a replacement does. In Avon, gas appliance work is permitted through the plumbing and gas inspector, and installing or altering oil-fired or other fuel-burning equipment needs an Avon Fire Department permit. Both are filed online in PermitEyes, since the town no longer takes paper applications.
Clear a path to the boiler or furnace and the oil tank before the technician arrives, and have the model and any error codes written down. If the old unit has to come out of a tight basement, ask whether replacement can wait for daylight while a temporary fix keeps the house warm.