Ceiling first. No debate.
The logic is simple: gravity. Paint drips, rollers throw a fine spray, and you'd rather all that mess land on a wall you're about to paint anyway than on a freshly finished one. Work top to bottom — ceiling, then walls, then woodwork and trim last — and you never have to worry about ruining work you've already nailed.
The order also sorts your cutting-in for you. When you do the ceiling, take the roller and brush slightly down onto the wall at the corner — a centimetre or two is fine. Then when the ceiling's fully dry, you cut your wall colour in crisply up to that wall-to-ceiling line. That clean junction is what separates a tidy job from a dodgy one, and doing it in this order means you're only ever cutting in once against a dry, finished surface.
For ceilings I'd reach for a dedicated ceiling white that goes on with a slight tint and dries flat — Little Greene's or Dulux's trade ceiling whites both do the job. If you want the ceiling to feel part of the scheme rather than a default brilliant white, a soft off-white like Farrow & Ball Wevet or Pointing keeps things gentle without going stark. A bright white ceiling over a coloured wall can read quite cold and clinical, so a warmer Slipper Satin above pale walls is a lovely trick.
The one "but what about" — what if you're papering? Same principle: ceiling paint goes on before the walls are papered, because hanging paper to a wet or unpainted ceiling line is a nightmare.
Practical bit: let the ceiling cure properly before you start cutting in the walls — overnight is ideal. Mask the top of the wall with FrogTape if your hand's not steady, but a good angled cutting-in brush and a loaded-but-not-dripping brush beats tape for a clean line every time. And do your woodwork dead last, once walls are dry — trim's the easiest to wipe overspray off, so it takes the hits.