Personally, I would opt for the 20"W x 31"H recessed. I prefer recessed medicine cabinets or flat mirrors. I think 20x30 would look fine with a 30" wide vanity. It won't be square like your inspiration picture, but rectangle looks good too. I have two rectangular pivot mirrors in two different bathrooms, one is proportionally narrower than the other and I like both.

The sinks are about 18 inches across (I just double checked and the vanity is 71"). So 20 would be closer to the sink size...

We have a very similar cabinet (ours is from Rejuvenation) that is 17" interior, 24.5"w x 29.5"h exterior that fits pretty perfectly over a 43" counter/42" vanity with sconces on either side. For a wider vanity, I might try to make it a bit wider for more storage, but that's tricky with proportionality, especially with 8' ceilings. (Ours are 9'.) I'd ask the cabinetmaker if they have photos of similar cabinets with wider dimensions to be sure you like the aesthetic as it widens. You could also just give the extra space to the sconces, but it's a bummer to lose the storage.

We have a more traditional aesthetic for ours but did a single door (interior width 17") over the sink for our 42" vanity, with sconces on either side. That size feels about right as far as organizing things in the cabinet, so I'd probably lean to three doors if you want to fill the entire space above the counter. If it exists, an ideal layout for me might be 18" in the center with 12-13" side doors. Not sure if either would work for seeing the back of your head, though. (You might consider a cabinet with interior mirrors for that.) Lighting seems to be a personal thing--I much prefer sconces on the side and it was a much better fit with the style of our home, so we designed for that. But there are lots of lovely examples with lights over the medicine cabinet or with integrated lights and they seem to work for people too. The mirror on my cabinet would likely be too small for some people, but works well for our needs. (We had an existing cabinet the same size so already knew we liked it--on a project with far too many decisions to make, I was happy to just order a matching cabinet for the new bathroom!)