3/4" works for most folks.
You can get more lumber in the kiln with thinner sticks, but the drying will take a little longer. Bassett (WDKA procedings in late 60s) suggests that the total production capacity is more or less unaffected because of this.
A New Zealand study concluded that 5/8" or 3/4" gave about the same production and drying quality so there's probably no reason to have thicker stickers. Thinner stickers may break more in machinery so they suggested using the 3/4".