For a first 22LR the Marlin Model 60 is the best option. You just sight it in and start shooting. There isn't much you can do to a model 60 that will be improvement. The dovetail scope mount leaves a lot to be desired. The aftermarket stocks suck.
After you have embarrassed a bunch of people with tacti-cool weapons. A 10/22 is in order. You don't need to do much to a 10/22. Replace the recoil buffer to get rid of that awful clack and mount a decent scope on the 10/22. I don't see how the bull barrels help very much. Out of the box a 10/22 will hit a squirrel in the head. I don't hunt ants so more accuracy isn't needed.