What water:cement:sand ratio gives the strongest mortar?
The less water the better, to a point. Excess water will weaken the mix. At some point in the other direction, there is not enough water for the hydration process(around 0.25:1 water:cement). In general though, to have a workable mix, there will be enough water for hydration. Use as little water as possible to make a workable mix, around 0.45:1 is fine. Don't use mortar for bulk fill, it's a waste of cement. The gravel in concrete is just filler, saving cement.

The concrete you mixed is sort of the standard DIY ratio, I don't know why it didn't work. While 0.5" gravel is a bit small, it can't be the reason for crumbling. Perhaps the cement was old? It may have absorbed enough humidity to partially hydrate, but not so much that it bound together.