The order is top down so drips and spatter will not ruin the finished work.

Typical order,

Ceilings, walls, Trim.

Being a painter for many years, we like to do the ceiling first because we bring a 1/8 inch over lap onto the wall with the ceiling paint, then cut the wall into the ceiling, the 1/8 inch overlap can provide for any imperfections in the wall or ceiling.

The best time to do it is post close so you don't delay the progress on the house and cost yourself in delays and added interest on the loan. Let the pros do the single color. It will be a fine base and at least it will be done.

I would paint walls after ceiling. We always have done our own painting and the ceiling will splatter some on the walls and that will be frustrating after you've put all that effort in.

I know moving and thinking of painting would be a royal pain BUT if you had even 2 full days (I mean FULL) you could knock it out. One coat one day and the final coat the next.

Can you get in there on a weekend after they have done the ceilings? That would be doable, you aren't in their way and you aren't working around half unpacked boxes.