It depends on what you want, fruit or a shade tree . We deal with around 2500 trees here so our pruning program is different then most.
In your case take out the suckers first, then any branches that cross over each other after that just shape the tree like a xmas tree, longer branches on the bottom and shorter as you go up. After pruning, spray with a dormant spray and you are set. By the way a tree that is taken care of will last 20 to 30 years easy. If anyone is interested in learning we start pruning the middle of January