I think all three faucet heights for an island installation are appropriate when you have a cathedral ceiling. I am assuming a fairly open floor plan.

Ceiling height makes no difference. Choose the one you will enjoy looking at, using fifty times a day .. Also the one you can slide your largest pasta pot beneath! More important, make certain you've got an air switch button for your disposal, to match the faucet finish. : ) on your island top. You touch that quite a lot as well, so no need to reach....or to dig under a sink cabinet door to grind, when you can have the easy peasy

We're going to have a pot filler behind our stove so pots will be filled there.

I've never had an island before and the faucet is so central and prominent that I want it to be aesthetically and functionally pleasing.

You can choose what ever you wish to go there. It's not a rinsing sink or similar as a lot of kitchen islands will have a small scale sink for more of a goose neck.

There is no, "appropriate faucet". It needs to be appropriate to you and your kitchen design is all:

Your ceiling plays no roll in this. What works with the counters/backsplash/YOU. That's what is most important.

You haven't posted any photos for those here so hard for anybody to offer suggestions. There is not right or wrong, just needs to work with the kitchen as it is designed and be functional is all.

You're over thinking it. More important that the pot filler and island faucet share similar styling and finish...................and that both suit your kitchen style and YOU.

Do not shop online. Go to a quality local plumbing supply catering to kitchen and bath!!! .Stay out of the big box stores.

I think you're right about overthinking . There don't seem to be any design "rules" I'm missing. I will make sure finishes and style is consistent throughout kitchen. I think I can take it from here. Thanks for the input.

By the way I did go to the "Plumbery," a local plumbing supply store. Great selection and knowledgeable sales staff.

Jan is correct about the air switch likely one of the best features of my new kitchen. With an island sink there is no wall for the disposal switch hence the need for the air switch otherwise you need to bend down under the sink to turn on the disposal.

You can get an air gap in the same finish as the faucet too. If dishwasher in island.

High enough to get your biggest pot underneath, it all depends on your needs

I have a low wall in my kitchen and my new faucet and light fixture seem too close, trying to see what the cheapest fix is

Chris, I did. Can you confirm your email address and phone number. Thanks