Hi, Amy.
I'm no expert or qualified orchardist, but here's what I do...
I feel that our yard trees should present a decent shape overall, so first I try to gauge which areas are out of symmetry (if any) and keep that image in my head while I look for and prune away any broken branches or deadwood. I'll then remove any suckers that are present from the ground up to the main scaffold branches. After that, it's time to get up into the canopy and find branches that are heading more up than out, or are crossing/crowding others. I like to remove just a few all the way back to the main branches or trunk in each section, then move on to the next until I've been around the entire tree. While you're up there, also think about creating enough elbow-room; it's easier to do later health inspections, disbud and harvest if you have enough space to maneuver (swivel around) in at least two directions between limbs.
I wouldn't suggest removing more than a third of the branches in any given year, but don't be afraid to cut away what's obviously too densely filled with tiny branches or too long and flimsy to support the weight you assign to it. If you want fewer but larger fruits you'll need to remove all but one or two forming fruits from each cluster. If you don't remove any the fruit can be plentiful, but usually smaller.
I don't think flavor is enhanced much if any by pruning/reducing, but the fruit is probably juicier if reduction is done.
I don't spray my trees with chemicals. Some years I have great apples and some years the bugs get a lot of them, but that's just my own personal preference.
