If you have surging idle wierdness it could be a vaccum leak especially since you say you have cracked rubber boots in the PCV system. Everyone jumps to IAC which in your case could be true since it sat for so long. Give the IAC a cleaning but I would take a can of carb cleaner and start spraying it around the engine bay to look for a vac leak. If the engine RPM flucuates when you spray in a certain area while the motor is running, you have a leak. Those kind of leaks can be non-existent at idle when the motor is cold so get it hot so the rubber expands.
Also, since the car sat so long the thermostat could have gone bad but it sounds like you are replacing it anyways.