I got great, heavy duty, chunkier ones from restoration hardware. I had initially purchased some like you have posted from home depot, but the quality paled compared to rest hardware, so I returned them.

Both your hooks are fine, although I do prefer the 3-pronged ones too.

I installed a rod with hangers in my mudroom so that coats could hang properly.

I like the three-pronged hook too. in terms of sturdiness, I think as long as you get one like the ones you posted, and the cabinet maker puts it up right into the studs, you'll be fine. FWIW, I bought a row of hooks to hang in our foyer as a placeholder until my DH builds a set of cubbies there, and when he put it up he somehow forgot to nail it into the studs. But we've been hanging backpacks and jackets on it and it's been fine (so far)

I think the 3 prong. Usually, you hang the main item on the long prong. Yes, you're over-thinking it too.

We're doing a mudroom with lockers.

The cabinet maker said the customer typically chooses the hook. maybe I'm overthinking this, but where do I buy the hooks? How do I make sure they're sturdy enough to hold winter coats, backpacks, etc?

And finally, what do you think of two prongs vs three prongs? The bottom two prongs on the three-prong looks a little skimpy...