I keep motor start capacitors for the blower, fan, and compressor on hand. Those are the failures I've had most. I've got Traine heat pumps at both houses and have replaced a small circuit board that controls the blower motor on both - same issue both times which is a resistor on the board (part of the blower relay) overheats, damages the board, and screws up the solder connection. I've got both boards which I can repair, but with standing the resistor off and trying to minimize the heat damage. Like you; I'm not fond of calling somebody to repair my AC and heating unit.
The other one is garage doors and openers. Right now the tensioner on my garage door (Wayne Dalton - not the normal type springs) broke and my car is trapped in the garage. After the weekend when the predicted stormy weather goes away, I'll deal with that. But trying to lift a heavy garage door with no counter balance and no handle isn't something I'm looking forward to. The Wayne Dalton tensioner springs are in the $200+ range. Seems like it's always something.