What species of fox makes the best pet? The answer depends as much on the owner as it does on the fox. As with breeds of dogs, there is no one "best" species of fox, only foxes with differing traits and needs. However, to make things a little more clear, I will offer a comparison on the different species to the best of my knowledge. In the interest of full disclosure, I have only personally owned reds, so I can only pass along what I've heard from the owners of other species.
Reds tend to have more laid-back and doglike personalities than the other species do (given how hyper Gizmo is, I hate to think what the -not- laid-back species are like.) The main downside to reds is their size (large compared to the other species; I know of a domestic red that's 25 lbs and not fat) and that they are one of the stinkier species.
Next up are Arctic foxes. I have heard more reports of aggressive behavior about young arctics than any other species; if I get an e-mail in my inbox saying "help! My fox kit is biting and I don't know how to make her stop", 9/10 times it's an arctic kit. I don't know if this is a specific stage that arctic kits go through, or if the aggression persists into adulthood. If anyone has more information on the temperaments of adult arctics, please let me know. However, if you are considering bringing home an arctic, it is worth noting that arctics are more temperature-sensitive than other species, so you'll need to make special arrangements for them in the summer to be sure they don't overheat. Arctics are also relatively strong smelling, from what I've heard.
As for fennecs, they tend to be a bit easier for new fox owners to handle because they are so small. 3 lbs of fennec is a lot less intimidating than 17 lbs of red fox. However, I have also heard that they are the most temperamental species, and have the biggest personality change as they get older. (They are also incredibly noisy. Not sure I could deal with this every morning.)
The remaining three species you can find in the pet trade are grey foxes, swift foxes, and corsac foxes. From what I've heard, all three are relatively well-suited to be pets. They're not as big or smelly as reds are, and aren't as high-strung as fennecs. I'll admit that I haven't personally kept any of these species, but I have heard nothing but good things about them. The breeder who I purchased Gizmo from has said that greys are her personal favorite.
More important than species, though, is that you get a bottle-raised kit. They need to be pulled from the mother before three weeks of age and bottle-fed by humans to imprint them on humans. Otherwise they will never be quite as tame or as friendly. For your first pet fox, it is very important that you get one from a breeder who bottle feeds.