If you use lights inside the cabinet I think you will need glass shelves. LED puck lights are probably enough inside the cabinet.
There are low profile LED lights that are pretty good over a sink. They mount on a 4" octagon deep box. Keep the number of conductors in that box to two.
Pot lights in the kitchen are still fashionable but really hard to lay out. I'm slow at it and it can take me hours to figure out where they have to be to light the work surface, light inside the cabinets, centre the beam on the cabinets or the doors, light the entire kitchen evenly, miss rafters, have enough attic height and look symmetrical. My typical kitchen pot light layout is a mess of compromises. Then, it takes time to ensure a good vapour barrier (Canada). It's a part of the reason that I turn down most residential work.
