Any pressurized carb cleaner will work. Buy the stuff at Walmart because it's so cheap and get 2-3 cans just to have on hand. If you have a lawnmower, you need some around anyway
You have to be a little careful with poking anything into the orifices, even brass, because it can stratch if you're too man-handed.
Based on the symptoms you've described, I would say you definitely had a leak somewhere in the system. Giving a good cleaning is going to be beneficial in the long run, but I don't know what you will stumble across what was making the slow idle-down problem to start with.
There are only 2-3 vacuum hoses that you would need to check. And the rubber connectors at the carb inlet and outlet are known to deteriorate over time, which would be a place that air can sneak in.
Let us know once you get it all buttoned back up and running again. Once you do, blip the throttle. The behavior of the idle after you blip the throttle will tell us a lot.