Prayer > Barrows > Moons order?

I'm currently 62 prayer, 65 att, 75 str, 70 def, 78 mage 71 ranged.

What would be the 'right' order to do these?

I could get 70 pray via green drags first, to get the hard mory diary and then start barrows for some tank gear, and then do moons with that tank gear.

But I could also do moons first and get 70 pray that way, then do barrows.

I could also do barrows without mory hard just for tank legs (but could go dry because I'd be hunting for a specific item), then do moons for 70 prayer.

What do people usually do regarding this? Any ideas?