trigger time and practice. you already have three good candidates for practicing. each has their own unique personalities that will do you well for practicing to shoot longer ranges. practice with what you have first, then move up to something else as your experiance increases.
the 10/22 will be good for learning to shoot small groups at reasonable distances and very cheap to practice with.
the AR15, same thing, with a decent scope, you can move your distances out further than the 10/22. still one of the cheapest centerfire calibers to practice with.
the Mosin, with decent ammo and a good scope, this rifle could reach some very long distances. has been proven in the past that it ahs the potential to go accurately at long distances.