The oil burning furnace really does need annual maintenance; you've got oil filter, nozzle, tuning, i think belt drive is more common in oil so you have a belt, blower motor that needs lube. (the direct drive ones are sealed to my knowledge)
You can get annual cleaning if you want without the contract, it may work out cheaper even if repairs are needed. Your call.
Make sure that the first service includes pulling + cleaning the furnace blower, cleaning the outdoor coil.
On the invoice for a/c temp split, pressures, temperatures, superheat/subcooling readings, amp draws should be checked and ideally noted on the invoice - otherwise you're not getting what you're paying for.