I put some cheap Ikea lights under mine and they are great. They are little halogen lights about the size of a hockey puck and they all connect together. I was able to use the outlet inside my cabinets for my overhead microwave so no wires are showing.
Like these except mine are hidden in a recess and don't look like ****.
http://ikeahacker.blogspot.com/2008/08/improve-your-kitchen-counter-lighting.html
Don't overthink it, they are just lights under a cabinet.