Oh my gosh, I love that photo! I would make the living room vaulted with a center beam and beams coming down to the top of the stone wall. And wouldn't you know, I couldn't find anything to show what I mean. But something like this, except a center peak, not a flat area at the top.

{{!gwi}}

What a classic look you will have in your new home.

I'd say a ceiling height with such a wall should be about 10 feet in the living room, and probably in the kitchen as well. That has a massive look to it, and the arch to the kitchen gives a definite rounded shape. I would think about a sort of barrel shape in the living room to echo that archway.

I saw a similar plan which had the big supports between the living room windows, which were lined up on two walls opposite each other. The space between the windows (which went down to the floor, incidentally) were sort of half columns, but built out for display spaces with lighting up. The up lighting shone on pieces of the beams which were revealed tothe sides, but to the middle disappeared as the ceiling curved. So you might say this was a coved ceiling. sort of? But what I like about it, is it repeats the curved arches, which is a strong pattern. While I like a vaulted ceiling in general, I think the vault would have to be like your archway to look appropriate for the space.
If I find my inspiration photo/house, I will provide the link here.

Y'all both have great ideas, thank you! We go with our builder tomorrow to meet our Achitect and I will show them your ideas. This is our first and only build, so I am just scared I will make decisions and later down the road regret it. I think that's why I'm having such a hard time making decisions. Thank you again!