The filter needs to be running 24/7 as it is what processes harmful ammonia waste into mostly harmless nitrate (after you have cycled). Make sure you have the outlet pointed so it ripples the surface of the water as this is what will keep the water oxygenated so your fish can breathe.
As long as the surface is rippling, there will be sufficient oxygen so the airstone isn't actually required at all, so you can have it on as much or as little as you like.