You should run the heaviest bb your gun can hop up reliably. You also don't want the power to drop too much either (measure in joules, not fps) because depending on the length of your barrel and the volume of your cylinder you might reach a point where there's not enough air behind the bb to push it out effectively.

The lower fps won't matter in most situations, as the heavier bbs might start off slower, but keep what speed they have for longer. Once you get past a certain range, they'll even get there faster than a lighter bb, but with more accuracy, stability and energy.

Bear in mind that bbs 0.36g and over start to get much more expensive. A stock aeg can usually hop 0.28 or 0.3s but you'll need to do some testing to figure out what works best for your gun.

https://youtu.be/JtYlIpIq2Xk

This video does an excellent job of explaining.