Most people paint them the same color as the trim. The comment about the island is nonsense. Go search for photos of houses that look like yours and see what you like.

Ugh, this site is glitchy and replies not going through!

Yes, most people paint them the same color as the rest of the trim, unless you really know what you are doing and have a very specific design theme.

Do not take design advice from a builder.

I have never heard of matching all the interior doors to the island color! If you have to ask here, then you definitely should not be listening to your builder's odd design choices.

Here is what most people do with matching trim and doors. Keep things consistent.

White trim and doors

Transitional Living Room · More Info

Wood trim and wood doors

East Valley Estate · More Info

Gray trim and gray doors

Castlewood Dr. · More Info

Should we leave the ceiling white as well (trim is all white), or paint it the color of the walls?  I should note that there is crown molding that will be painted white as well.

Keep it simple and classic. Do the ceilings in white too.

I like to use semi-gloss paint for crown, trim and doors.

Flat paint for ceiling.

Matte paint for walls.

Yes, some people like to paint their ceilings in a different color or in the wall color, but again, that is usually part of some specific design scheme.

And painting ceilings is hard, so it is much better to keep them white and still be able to change out the wall color if you want to repaint some of the rooms as you decorate down the road.