I'd say 15mm is more common, but 19mm is found on many many RedOne cameras. You can have 15mm or 19mm rods with the Red because you purchase the base-plate it will use. I'd go 15mm. I've never, ever understood the advantage of 19mm rods.
The camera isn't supported by the rods, it's supported by the baseplate. Which is just a chuck of metal screwed to the camera.
Things like a mattebox, follow focus, pistol grips and lens supports are found on the rods. All of which, are the same weight or lighter than previous film camera versions.