Matte black.

Agree matte

Do you think my ceilings will be tall enough where it doesn't make the room feel small?

Unless the room is huge, I don't think it should be a problem.

The room is actually really big. It's a open concept. Its the living room and kitchen with Breakfast nook. And also the ceiling above the living room is a trey ceiling.

I wouldn't do it, regardless of the ceiling height, but here are some photos to show you how it might look:
https://www.houzz.com/photos/black-ceiling-phbr0lbl-bl~l_1617

So, if you have a tray ceiling below it, are you going to paint the upper ceiling black and the lower one another color? I am not advising against using black in a large room - it's just that the size of the space has an effect on how much ceiling you see. One of the virtues of a black ceiling is that it feels invisible, making the space seem larger. To the extent that the space is larger in plan, you see more of the ceiling, and so that makes the strategy somewhat less effective. There are unfortunately no hard and fast rules here. :)