River Rock? Hopefully you are talking about larger than river gravel sizes. I suggest a range from 1" to 12" rocks, mostly on the larger side of that range.

I went from a foot above the full pool water line (diagonally up the bank) and 18" below (vertically downward wrt to water depth). This works well as my pond has not dropped more than a foot during any dry spells. Consider your water fluctuations and apply rock appropriately. I'd give it an extra foot below the lowest water level. I do have to admit that it seems like the rock that is normally exposed above the water has crept into the water some as the last 4 years has gone by. I guess it's settling and, maybe, sliding down the back some, but this can easily be added to compared to adding rocks at the under water side.

Having rock below that 18" mark (down into 4 foot of water) in several places will also be good for the smaller pond inhabitants if you can spare the rock.