What connects them
All three fail in the same place on a cheap version, and it is never the place you look at in the shop. A bread box fails at its seal, either sealing completely and turning the crust to leather or not sealing at all. A lame fails at the blade holder, which loosens until the blade wanders mid-cut. A peel fails at the joint between blade and handle, or it does not fail and simply never gets used because it lives propped against a wall.
So the decisions here are about the part that breaks rather than the part that photographs. Vent holes punched where you do not see them. A curved arm that holds the blade at an angle rather than square. A handle that folds so the peel fits in a drawer.
Where to start
If you buy bread rather than bake it, the bread box is the one that changes a week. If you bake, the lame is nine dollars and it is the difference between a loaf that opens where you meant it to and one that tears out at the side.
The reasoning behind both is written out at length: how to keep sourdough fresh, and why dough sticks to a metal peel.