Hi Sliz,
This tree may have never been pruned to any specific shape in mind, so it’s developed a lot of weak crotch angles that ultimately threaten to break scaffolds off if fruit loads get too heavy. That lower larger branch growing up to the left off the main trunk is an excellent example of a weak, undesirable crotch angle. Several of the larger ones up around 8’-9’ high also are weak and should be removed. It also seems to be following the call of the sun as it grows towards heaven! So those to me seem to be your greatest challenge. You may not find guidance that tells you exactly what to do, but I’m posting several references that provide examples based on age of the tree.
Since tall trees only get taller unless topped, I think this is your first decision: I would top both at a comfortable reach of about 7-8’ high. Then I would look for and mark those lower branches that are growing nearly horizontal; these are you strongest ones to preserve. Then I would prune off all those branches below about 3’-4’ high and all those with acute angles wanting to grow more vertical than horizontal. My goal would be to train all the stronger branches you save so they can be trained over about 2-3 years to completely fill in the full circle around the trunk to maximize sun exposure and assure that the upper branches are not casting a shade over lower branches. Ultimately an open vase, not central leader will be achieved.
I would wait until springtime to make these pruning cuts since you will be leaving large scars that can more quickly be covered with new spring growth.
Dennis
Kent, Wa
Pruning a Young Peach Tree
Pruning a Two-Year Old Peach Tree
Olpea’s pruning advice and video: Note pruning while in bloom!
Virginia’s illustrated Peach tree pruning based on age of tree, very good: