Various low-powered rounds, and a collection of .22 short ammo. This got me started looking at 22 rifles that will shoot anything. My model 60 only functions well with high-velocity 22LR ammo.
What I wound up choosing is Marlin's bolt-action counterpart to the model 60, the XT 22TR tube-fed bolt action. I say it is the counterpart because it appears to have a very similar barrel to the model 60, if not the same. -Fairly heavy for a 22, and finished nicely.

It will fire .22 S,L, and LR interchangeably, holding up 25 Shorts in one loading! I tried all of these, and only the Shorts had a quirk... You have to hold the rifle level, and work the action briskly in order to reliably eject the short cases. If you do that, it works very well.
I intend to always fire the same high-velocity load, and occasionally shoot the low-powered stuff as the occasion calls for it.
The Marlin XT 22TR is more accurate than my model 60 semi-auto. It has a much better trigger. I have had bolt-action 22 rifles pass through my hands many times, and got to shoot a few, but this is my first one to own. I am very pleased with it, and intend to invest in a nice peep sight for it.
More on this rifle soon.