The order things get used, which is not the order they get bought
The typical gift set is a stone, a wheel cutter and a flimsy peel. In practice, the order in which these tools stop being frustrating is almost the reverse.
First, a bench scraper. The cheapest thing in this entire site, and the one that changes the most about handling dough. It divides a batch into balls without deflating them and lifts a sticky ball off the counter cleanly.
Second, a scale. Not because precision is virtuous, but because it is the only way to make the same pizza twice and therefore the only way to learn anything.
Third, a peel you can actually launch off. See the peels hub. This is where most people are losing pizzas.
Fourth, the baking surface. The biggest single upgrade, and also the most expensive and the one most likely to be the wrong size if bought as a surprise.
Fifth, an infrared thermometer. Which sounds like an indulgence and is the item most likely to produce an immediate, visible improvement, because almost everybody is baking colder than they think.
Buying a gift without knowing what they own
Three rules. Avoid anything sized to their oven - stones, steels and large peels all depend on measurements you do not have. Avoid duplicating the obvious - anyone making pizza already owns a cutter of some kind, so a better cutter only lands if it is genuinely better rather than merely newer. Prefer consumable-adjacent and small-tool items: a bench scraper, a small precision scale, a good thermometer, proofing containers, semolina. None of them are exciting to unwrap and all of them get used within a week.
Cutters: the specification that matters is what it does to your surface
Almost every cutter comparison is about blade sharpness and topping drag. The more important question, if you own a stone or a seasoned steel, is whether the tool presses metal into the surface you cut on. A 14-inch rocker presses its whole length down; a wheel drags a hardened edge across; scissors with a spatula base keep the blade off the surface entirely.
None of which matters if you transfer the pizza to a board first. Which is the honest answer for most people, and the reason we would not spend much here.
What we would not buy
Novelty gift sets built around a thin ceramic stone, a stamped peel and a plastic cutter: the stone is the part that needs to be good and it is the part they economize on. Dough-rising baskets sold for pizza, which are a bread tool. Anything with a countdown timer built into it. Branded flour tins.