I want to add that the brackets will definitely be screwed into studs, the ledger will be hit and miss (will use drywall anchors where necessary). Do I need lag bolts for the brackets, or just big screws?

Cutting U-shaped shelves will probably be more trouble than it's worth. You'll find that walls aren't flat, the corners aren't square. It would require a finicky templating process to get the shelves cut to the right shape, and then it would be awkward to get them lifted into place.

Dishes and wine can be quite heavy. No, three brackets per U-shaped shelf won't be enough. Drywall anchors are pointless for such loads.

I might skip the brackets altogether. Instead, I'd rely on the ledger for the backs (use a stud finder), stiffen the front edges of the shelves with a 1x2 on edge, and support the fronts with vertical posts that go to the floor. The oak brackets could work, but it would take at least four per level.