I have a very extensive collection of tools from years of working on everything from airplanes to heavy equipment. For chainsaws, most of the necessary tools could fit into my pockets if I had a good belt on...
A 4 piece set of the cheapo orange handled picks from HF is something I use very frequently. These have a straight pick, a 90 degree pick, a question mark shaped one (used for fishing fuel filter/lines from the tank) and so forth. They run a couple bucks or so. An air driven butterfly impact is another frequently used tool. I take off clutches and flywheels with it. I have never in my life used a piston stop of any sort on a chainsaw. Just hit the clutch with the little impact and off it comes. Another very frequently used tool is the Mityvac pressure vacuum tester. Not only to check for case leaks but also to verify the integrity of impulse and fuel lines (installed or not)
A cordless drill driver is used regularly to put screws in and out. Saves lots of time.