Hire a designer. 16’ is not remotely user friendly to human scale. You’d be better off creating a loft space.

Laura, you are not alone being confused by this; what metric to use to figure out sufficient lighting with the added complexity of having high vaulted ceilings, which means the lights will possibly be mounted way up on the ceiling.

Where to start: both NKBA and IES recommend 50 foot candles on the kitchen counters. Foot candles ( 1fc = 10.76 lux) are the only metric that matters. LUmens are a measurement up at the fixture, not delivered to the work surface. The type of lamp (bulb) you pick has an ENORMOUS effect on delivered footcandles; I"ve seen at 15 to 20 times improvement by switching from BR floods to PAR spots. I've written about this topic quite a bit for www.proremodeler.com. Look for lighting articles by Doug Walter.

But in addition to task lighting, you'll want some large decorative chandelier type fixtures for ambient lighting. Wood ceilings and walls absorb a tremendous amount of light! See if you can't shine lights not only down, but UP onto the ceiling.

My guess is you're probably going to be best working with some sort of suspended fixtures; pendants or hanging track, as much as I dislike track because of it's tendency to shine light in peoples' eyes if its aimed anywhere but downward. A lighting designer would be a good investment, preferably one with a certification from IES or ALA. Good luck!

This link is specific to their fixtures but it helped me and it does take into account the height of your ceiling. I just did the math based on the fixtures I purchased against the details of their fixtures. Then I rounded up and added a dimmer.

Lighting Calculator

That's exactly how I did it as well. And don't forget, all of the light doesn't come from the ceiling. There may be a floor lamp or buffet lamps or art lights, etc. -- you should add them all up for a total. And make sure you buy a gimbal version of whatever LED light you buy as your ceiling isn't parallel to the floor.

When in doubt more on a dimmer is better (in my opinion).

Good advice from Joe and tatts. How do you measure the delivered foot candles? There's an app for that! And most of them are free. I use Light Companion and Light Meter Pro. They use the camera on your phone; and I've compared them to professional light meters, and they're pretty darn accurate. To figure out how much light you can expect, you need to look at photometric charts from the lamp manufacturer, and you'll see a chart that shows graphically the inverse square effect the tatts explains above. If the light is at 8 feet, and the counter is at 3 feet, look at what promised light level will be at 5 feet away.