Well, like just about everything else - you talk to 100 experts and you get 100 different best ways. But the theory is thus - and may not happen in your area. Late frosts after prolonged warm spells are killers for peach blooms and young fruit. I gave up growing peaches around here just for that reason. Perhaps 3 years out of 10 would I get a crop because of late frosts after warm spells. Peaches like most fruits, have a chill requirement - meaning, they require so many days of cold weather to be able to produce a crop. Some varieties of peaches require more days, some require fewer chill days. If it is warm and their chill requirement is met, they will start the blooming process. Pruning is thought to especially trigger the blooming process. Theoretically, pruning in the dead of winter, would stimulate bloom development at the first warming spell, and the blooms will get killed at the next frost. Many small growers will wait until what is called "pink bud" stage - the bloom buds are just starting to swell and show some color - but still a few days until opening. Now, you talk to another grower, expecially big ones, and they have successfully pruned all during winter. There is no 100% correct right answer, just ones that should be better.
Training - don't want a central trunk, but an open "V" shape or vase shape with maybe 3 to 5 well-spaced main branches forming the vase. These branches should be roughly at a 45-degree angle to the trunk. You do not want a central leader, you want to leave the center open for sunlight and air so trim off the inward growing branches and any suckers or water sprouts that are growing upright. First trim off any dead, dying, diseased branches, then evaluate the remaining branches. I'd then cut off the inward growing and upright branches along with any water sprouts. Crossing branches that touch or grow from one side of the tree to the other should be eliminated. Even little branches that are growing inward should be pruned - little branches grow into big branches. Then finish off with trimming any sprouts from the lower trunk or rootstock. You want all the plant's energy going into the branches you have left above. When you cut off a branch - cut it just above an outward facing bud.
That will produce a peach tree that is not too large. But you can do things to keep a tree smaller - summer pruning. After you harvest the fruit, prune off your main branches by 1/3 or 1/2. Cut just above an outward facing bud. This will reduce yields from that tree, but will be much easier to harvest, and you can plant trees closer together, and might get more fruit in the same amount of space. With two trees, spaced well apart, I'd probably not worry about the size of the tree, unless you want to pick the fruit while standing on the ground. But if you want to grow a number of trees intensively, there are some interesting ways to do that - even espaliering.
