re: where to get some crushed limestone?

Crushed limestone is used so extensively that its widely available. Start in Laplace here...LINK /

If their minimum order is too big, ask them who is a nearby reseller. Even modest-size nurseries usually offer it.

Such a thin layer will be scattered by even lite foot traffic... make it thicker. In my experience smooth river gravel stays in place better and looks nicer. In a couple of years no matter how thick and what type you use, you will get a buildup of dirt in the gravel. That does lock the gravel in place but allows weeds/grass to invade. Plan on annual use of Roundup, pre-emerg and weeding. I have a friend in rural WA state who has a large gravel driveway. He cleans it with a propane torch normally used to heat asphalt road patches.