Hi Peter. :) Unless you're going very dark gray with tinted primer, I'd say straight to painting. Two coats should do it, especially with quality paint.

You could take your chances with not priming, however, if there are any crumbling issues or older stucco you will want to prime you could get faster color fading and your paint might not stick well if the surface is slightly chalky.

Unless your walls are very clean, with no nailholes, dings or gouges to be patched, and are void of scuff marks, sun fading, and differences in sheen from spot scrubbing, skipping the primer and going straight to paint rarely results in saved steps. You'll just land up having to put on more coats of paint.

If there are any repairs to be done on the walls, you'll be priming over the patchwork/drywall compound anyway, and going over the entire wall after the spot prime lowers the risk of "flashing," which is a noticeable difference in the paint sheen where repairs are made. Read up on it, because you definitely don't want it.

Primer is cheaper than paint. So, for a first coat, why not get all the benefits of a good primer base? Primer helps adhesion, and also promotes more consistent coverage, for a richer, truer read to the color.