Oil is recomended most often, but I prefer water. Oil makes a nasty mess, which gets on your hands, your work, and in your food if the knife is used for food preparation. You can take a stone that has been used with water, dry it out, and switch to oil. But once you use oil on a stone, you are pretty much stuck with it. Natural stones are more traditional, and often more attractive.
Artifical stones are more consistant, and usually cheaper.
The Vikings selected their whetstones for beauty as well as function. They were often selected for colorful contrasting bands, and sculpted into elaborate shapes. They apparently served some ceremonial proposes as well, because some of the largest and most elaborate examples have been found in connection with royal burials, and in unused condition. In one of the Nordic legends a giant used a club-like whetstone as a weapon against Thor. Soft Arkansas Stone I have a small stock of natural Arkansas stones with an attractive rose and cream color patterning.