Start with the list that belongs to you. Changing the filter is the highest value thing a homeowner does, and nobody needs to be paid to do it. Thermostat batteries are next, and they cause more January no heat calls than most people would believe: a thermostat with dying batteries can behave strangely for weeks before it quits, losing its schedule or failing to call for heat on the coldest morning. Keeping supply registers open and return grilles clear of furniture is yours too, and closing vents in unused rooms is a myth worth abandoning.
Clearing the outdoor unit is also yours. Rake leaves out of the coil, cut the shrubs back, keep two feet of space around it, and kill the power at the disconnect first. Use a garden hose on gentle spray, not a pressure washer, which flattens the fins. Resetting a tripped breaker once is reasonable too: fully off, then firmly on. If it trips again, stop. A breaker is telling you something downstream is drawing too much current, and repeated resets remove the protection while the fault gets worse.