You've got 3 main options with regard to undercabinet lighting. Halogen, xenon, and fluorescent. Halogen and xenon have about the same color and type of light, however xenon does run cooler. We all know what fluorescent looks like.
Your "warm and inviting" and "not reflective at night" seems like it can best be met with fluorescent under cabinet lights. Halogen and xenon are quite harsh and not diffuse at all, but they are quite bright. There is some LED stuff making it to market now for this application. I have a feeling that it's expensive, and I have no idea what the color temperature and color rendering will be like. A great deal of other "white" LED stuff on the market now is remarkably blue in appearance.
Unless you have miles of countertop, you should be able to have this done within the 500 dollar budget. Just depends on your layout and how hard the fishing will be. Wait... I'm think you live in conduit land, right? Double everything. :cheesygri