I've used .410 , 20 and 16 gauge, and .22LR in a Glenfield Marlin Model 60, and a single shot lever action Ithaca... the 16 and 20 guage seems more productive, but I didn't like picking out the shot. My vote is for the Marlin .22LR.
Well I tell ya . For fifty years my go to squirrel gun is model 60 ( I also collect them ) . I used just about everything , my savage HMR is sweet I love the accutriger and can make head shots at 100 yards if there not running to fast but there heavy . I hate biting on buckshot . As far as ammo , I have enough in all my calibers to last the rest of my life and I just started reloading . Payforward and you do yourself good.
I have a scoped 10/22 and an imported clone of a Remington. Nylon 66 with open sights. The 66 clone was my first gun I had it since I turned 8. Length of pull is a little short for me but it has never failed me as long as my aim is good.