When asked "What exactly other than flexibility are the criteria for good sock yarn?" she responded:
Oh lord. That depends on what you want from the sock. If you really want to wear it like a normal sock, I would suggest Superwash (which is always wool). Superwash wool doesn't shrink and can be washed in the machine. It's also harder wearing. Most standard sock yarns are automatically superwash and are usually 65-76% superwash wool and the rest is nylon or something. There are some non-superwash yarns people use for socks, but imho these are more for pretty than everyday wear. Tara gave me a pair or merino wool socks and I use those around the house or just for work. I don't trust them to dog walking. They're too pretty for that anyway.You can find more of TheBlackSheep's purls of knowledge on her blog Misadventures in knitting.
Most sock yarn is also fingering weight. Cottons are the thinnest, as there's no need for warmth really. Then there's the normal fingering weight sock yarn (bog standard sock yarn), which is 4 ply here. Then you can get the thicker yarns 5, 6, and 8 ply for extra warmth and quicker knitting.
Now the sock yarn I got for my grandmother is Sooper Dooper sock yarn. It's snow and water resistant, 8 ply, totally unshrinkable superwash. It's very thick and luxurious. It also comes with reinforcement yarn for the heels and toes. This is basically a thick thread in the same colour that you just knit with the yarn, so you're knitting 2 strands and not just one. It makes the socks harder wearing. I will make sure I get the reinforcement yarn for the Aran Sandal Socks because the pattern is complicated and I want them to last a very long time. Normal socks I can knit when on the phone, these require concentration, which make it all the more important that they last.
Anyway, beware of hand knit socks. Once you have a pair, you won't want to wear anything else, especially in winter. They are some of the warmest socks I've ever owned, even if not the thickest or wooliest.