Ten to twelve pairs is a comfortable range for most school-aged kids, covering a full school week with spares for sport, after-school activities and the socks that inevitably go missing somewhere between the laundry basket and the drawer.
Kids socks get more wear per day than most other pieces of clothing, since they are on for the entire school day, sport practice, and often weekend play as well, so a slightly larger rotation than you might think necessary tends to work better in practice.
Buying most of your kids socks in one or two similar styles, rather than lots of unique one-off pairs, makes the sock-matching problem far more manageable, since a stray sock is more likely to pair with something else already in the drawer.
For kids who do organised sport, it is worth having a few pairs specifically set aside for that purpose, particularly if grip or cushioning matters for the activity, so your everyday school rotation is not being borrowed from constantly.