Tall spindle trees should require very little pruning unless the laterals are large in comparison to the leader (perhaps 50% or more), or are pointing straight up. Worst case you probably would not want to remove more than 2 of them. Cut at an angle and leave a stub to induce a new lateral to grow from the stub.
Training is a lot more important than pruning. Laterals should be tied down to a near horizontal position and the first few buds at the very top of leader should be rubbed off to reduce competition with the leader.
A few apples will help to pull the laterals down, but 10-15 apples is probably enough on a vigorous second year tree. Less apples if its not.
A comprehensive set of video on tall spindle apple production conducted by T Robinson of Cornell were recorded at the NC apple school a few years ago. Its the most useful information I have seen. Wish I had seen it before I planted my orchard!