I would definitely install undercabinet lighting. Rather than a strip under the shelf, some cabinet companies offer the puck lighting that fits flush into the shelf.

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Undercabinet lighting, and note how they are all concealed by a light rail in Wilson's examples. Because it's higher, you want to be sure it's either hidden or not unattractive. So not just a plain shelf like in your plan. We short people see EVERYthing.

You could also consider a complementary sconce over that sink if it works with your planned wall treatment but it doesn't look big enough.

(Be sure your recessed lighting lights up the main sink--that chandelier won't do it on its own.)

I say strip lighting too. You can get it housed in an aluminum fixture, frosted covering, and the pucks ( like mentioned above). Good luck. It will be nice. Be sure you get enough lumins for the area, it will be higher than the typical undercabinet lights, so the light will get diluted.

We have LED tape under the cab over the sink. It offers plenty of light. B/c those cabs are relatively high, we used a valance similar to the one in the white K above. All other undercab lighting is shielded by light rails someone mentioned above. If you really want strong lighting, consider halogen pucks. We used those in top cabs w/ glass doors for display. And they give a very white light.

Appreciate the input, under cabinet lighting seems like the way to go.