The best material for Pet Paintings is oil, and the material best suited for oil is and always has been canvas. Canvas 'drinks' the paint so the brush strokes are accurate and never shimmy. Furthermore, oil retains full luster.
Interestingly, canvas wasn't always the choice of professional painters. Before 1400 the main choice of the portrait artist, and other artists, was wood. Wood was good, it 'drank' the oil, but it was expensive to make and prepare.
Along came the renaissance, the world opened up, and new technologies were found around the earth. One particular technology had to do with the propulsion of sailing boats, and this was to prove a boon to all painters, and to this very day. That's right, that stiff canvas used to catch the wind and push wooden ships and iron men across the seven seas turned out to be the perfect replacement for wood.
Canvas was originally made from a family of plants called hemp. Hemp, as most any hippie knows, is another name for cannabis. The material was originally constructed by weaving the fibers of cannabis in a tight pattern.
Canvas was probably first stretched over the wooden planks currently in use; it took a while for wooden frames to catch on. This was probably around the fifteenth century, and the practice caught on like wildfire. Every artist who was any good, and a few who weren't, were quickly drawn to the new material.
As has been noted, canvas 'drinks' oil, but that was only the start of the benefits. Canvas was also lightweight, easy to move (ship), and much, much less expensive. Interestingly, because canvas is so easy to manipulate larger paintings could be made, and the size of portraits literally exploded.
The next big occurrence, in the history of this painter's medium, was in the type of material used to make the canvas. During the industrial revolution American Cotton was less expensive, and therefore became the artist's choice. It should be said, however, that the top tier of portraitists, the more famous artists, still preferred hemp, for it lasted longer, was stronger, and, here's something to consider, was less prone to the effects of mildew.
Today's canvas, preferred by professional portrait artists, is usually made of cotton duck, this because of the large popularity (and decreased expense) of acrylics in painting. More accomplished artists, which would be to say those fellows and gals who actually make a serious living through their work, prefer linen, and this is because the top notch painters work with oils. Whatever the medium, however, the true test is in the skill of the artist, and this especially holds true for the art of pet paintings.