I think those bench with shelves and hooks take up a lot of visual space, and it might not fit well in the places you have offered. I would hang a row of hooks without a bench, near the door, and a seat or bench near the stairs.

I agree. Both those spaces seem pretty smalI. The whole area seems tight with the stairs protruding there. If you have to have both items, split them.

After all, since you are just moving in you might find this door is not the best one for keys/purses.

Little Bug brings up a good point. It's not a smart practice, from a security standpoint, to stash purses and keys next to the door.