The sink might be a bit much -- I think it would be impossible to keep this shiny. You can find some quite reasonably priced antiqued copper bathroom sinks, however.
The entire kitchen might be a bit more than you would do in a "real" kitchen, but I think the idea of warm wood, copper accent tiles (You can find a variety of copper tiles with a quick Google search.), and black counters is really striking. A more "country" look would be to combine copper with white counters and backsplash.