We have a kitchen that measures 12'x13' with a vaulted ceiling....(pic included)?

Undercabinet lighting is usually additional lighting for task lighting. Halogen and LED are two good choices but halogen produces quite a bit of heat. You'll still need general purpose overhead lighting. You might think about fluorescent fixtures or pendant lighting. Low voltage lights are nice and will save money.There's a lot of options out there. These links are pretty informative.

You may be able to replace the track lighting fixtures to newer lighting.

Removal is possible with ceiling repair and another fixture.

Generally under cabinet lighting is an extra.

Lighting Types

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This site has same general Lighting Information

Yes you will need to replace the overhead lighting. My suggestion would be to have an electrician put in either a very nice hanging fixture or go with inset can lighting set into the ceiling. They make the type to go in your angle ceiling and can be directed. you will have the benefits of adequate lighting without the eyesore track.

why not see if you can change the fixtures on the track a more up date fixture might look sharp as they can be removed from track with a twist

you will still need area kighting as under cabinet is more accent lighting or work area lighting