HVAC general question

Get both inspected and cleaned to start with.

After that the most important things are filter changes, keeping the outdoor unit's coil clean, and monitoring condensate drains for leaks.

Once you establish a baseline with the a/c you don't need to get the refrigerant charge checked every year, but do need to call if you notice changes in performance or new noises.

Keep up with the filter maintenance on the furnace and the blower will never need to be cleaned or pulled again once it's done, or at least not for many years. Trick is using decent filters and making sure that air isn't leaking around the filter rack, bypassing the filter.

The furnace's heat exchanger should be inspected at least every 2-3 years and after the 10-12 year mark every year. Ditto for monoxide in the exhaust. Certain things like flame sensors may need to be cleaned annually, but there are lots of furnaces out there running which haven't been serviced for years. Annual service is a bit much.

The service contracts where you pay for insurance against parts/breakdowns are generally a waste of money - you'll be better off self-insuring. The contracts are a money maker for companies, because if the furnace doesn't break down they pocket $150+ (on top of seasonal maintenance) for doing nothing!

This is only my opinion and others, especially who do this for a living will disagree with me. (...but follow the money)

...the gas furnace without a belt drive doesn't need parts for cleaning, air/humidifier filters aside. The parts are for break-downs and you'll pay a pretty penny for repair parts, labour, and the service call.

Typical service call all inclusive for part break-down could set you back $300-$500 from the limited stuff i've seen, but then again that should only be every few years, likely more as it gets to 15+ years. (around the point where the parts/labour coverage isn't covered any more and they start trying to sell you a new furnace you don't even need. )

Insurance is a money maker, otherwise they would never offer it; it's gambling and the house usually wins. You hit the jackpot only if the furnace happens to need a costly repair the year you get the plan; averaged over several years you break even if lucky or lose.

You shouldn't be seeing a sub-10 year old furnace breaking down much at all, really. Back when they were all standing pilot, with no fancy electronics, thick heat exchanger, furnace may not break down for the first 20 years and last 30-40 rather than 15-25. But then you pay a lot more for gas instead of repair/replacement.