A 10/22 Ruger is a fum gun but it is not high on the accuracy scale. I have one, and I also have a Remington .22 pump. The remington is far more accurate, and consistent, and will also shoot the same .22LR cartridge about 1000 feet farther.
You are right about the Ruger 10/22s not being accurate at least as they come out of the box. They are accurate enough tho for nearly all purposes and people dress them up with match barrels and other things to make them shoot great.
As it comes out of the box, the cheap Marlin model 60 is a much more accurate rifle but it has a tubular mag which when empty, takes a long time to reload.
I would probably pick the 10/22 just for the fact there are so many mags and other accessories for it. You might even get lucky and get an accurate one.