The hands-down best way to light your counter work areas any place you have wall cabinets mounted over them, is with under-cabinet lighting. It’s a wonderful thing to have light shining right onto your cutting board, instead of standing in your own shadow!
You can do this several different ways, and there are more choices becoming available all the time. here are some ideas:
Incandescent Lighting: cheap, hot, good light quality, but an energy hog. You can still buy incandescent strip lights intended to mount under your cabinets, but I don’t recommend them – there are much better alternatives.
Halogen and Xenon: either puck lights (small round individual fixtures) or strip lights. These are moderately priced, the light quality is excellent, but they are HOT HOT HOT. Yes, Xenon is cooler than halogen, but it’s still scary hot – not just the lights themselves, but the 12v transformer they run off. Even if they don’t get hot enough to cause damage, who needs that extra heat in the kitchen in the summer? Not energy-efficient, either.
Fluorescent: strip lights in various configurations, some can be connected together to all run off one power hookup. Older-type fluorescent lights had an unpleasant light quality, but they are cheap.
Newer varieties have much better light color and quality but they are rather more expensive, comparable with halogens. They run cool, and are energy efficient.
LED: these are the up-and-coming thing in lighting. Right now the really usable fixtures are expensive but they have very good light quality (no blue-white cast like older LEDs). They run even cooler than fluorescents, have an even longer lifetime, use less energy, and don’t have the disposal issues of the mercury in fluorescents.
Right now, I’d say go with LEDs if you can afford to, otherwise fluorescents – or if you can possibly wait, do so until the price of LEDs comes down within reach.