I would paint the walls a warm toasty neutral, a light tan/mocha/warm "greige". Looks like you have some red/orange touches in the room. To add some pop, I would paint one small area a red/orange (like BM navajo red). Maybe just the wall that the small square picture is hanging on... And hang a nicely framed large piece of artwork or some large "pier oneish" plates for a little wow factor. I would leave the ceilings white. I think these colors will pull everything together and warm up the space. Good luck!

Are you adding trim molding? I like color on the ceiling, esp if it's vaulted. So I would paint manchester tan on all but the accent wall and continue it up around the angled part of the ceiling on all sides. Then paint the accent wall the greenbrier beige and paint the flat part of the ceiling the same color. It would look great if you have molding to break up the areas painted in the simply white to offset the areas. That may be too much for you so you can just paint the simply white on the flat and angled portions of the ceiling and then paint the walls manchester tan with the greenbriar beige accent. I'd suggest going to houzz.com and searching on tray ceilings so you can get some ideas of how they are treated with paint.

I would go with the 2700k for most areas. except for a study/ work area that would be used late into the night. A higher color temp impairs the production of melatonin which could result in difficulty sleeping. Use the flat ceiling can & trim if the angle is <= 15 degrees. The CR6 and similar lights (RT6, ...) tend to have more light spillage than the BR or PAR bulbs used in recessed lighting i.e. - less of a spotlight effect. Some people may find it tricky to get the lamps fit. If the ceiling is high - 10' or more, indirect / cove lighting may be more elegant and practical.

What else would you paint it with? I suppose you could spray it but what a mess. I always roll the direction the sun shines. Then if you do get a lap mark it will be parallel to the sunlight and less noticeable. Not sure what Christopher will recommend but I wouldn't do quadrants. If you need to section it, section the whole length to minimize those perpendicular lap lines where the light could catch them. Hopefully you don't need to do two coats lol. I used to have to do that when ppl smoked in the house. Hard to keep track. I've used painters tape on the wall and just moved it as I've done another stripe. Good luck!