Don't use ordinary crushed rock at 3/4" max size, commonly used for roadway base course. It can erode easily under fast flowing water, even if compacted with traffic. I know having had to deal with this for our local community under heavy flow conditions.
To stabilize uniform sand, which you may have there, I'd go for a layer of what we call "beaker run rock". This usually is well graded blasted dolomite from about 4" down to fines having been run through a rock crusher. It can be worked into that sand in layers to stabilize it also.
Once you experiment with thin layers on the sand, you will see what it takes to make it stable. I'd guess at least 6 inches.
In this area some communities use this for a base layer upon which they later spread the 3/4" gravel because breaker run is difficult to blade smooth.
If you have no such quarry rock breaker run, maybe coarse gravel, with cobbles and boulders run through the crusher will also do it. You need the big sizes in the mix.