As a former paint technician, I used to be a firm advocate of "stirred, not shaken." However, it now depends on the paint and how it's packaged.
Some paints, if shaken, pick up a lot of air when shaken, making brush painting or volume measuring difficult. If it comes in a dropper bottle, this is not a problem.
Glass bottle, like Tamiya or Gunze—stirred.
Dropper bottles, like Valllejo—shaken, after adding two small stainless steel balls. (Don't use BBs!) I bought a paint shaker, mainly because of arthritis, and it is faster as well as less painful.