@The-Cartesian While leveling, you will have very little bonus healing or none at all. The way the game is designed, HpME or Heal per Mana Efficiency increases with spell rank. In other words, your most recently trained spell rank will be the most efficient. However, the higher the rank, the higher the mana cost of the spell. That being said, It would be prudent to know how much each rank heals your tank for and wait until he loses that much or so HP before casting it. In this way, you will be the most mana efficient. I know this seems counter-intuitive and may even scare your tank but he/she will get used to it during the Dungeon. Now, with large increases in spell power, the HpME relationships can drastically change as the percent difference spell power provides is much larger the lower the rank of the heal. But that is another topic for another day.
It seems like you are focusing on leveling in your question. In that case, try to use the highest rank unless you need to use a faster heal for an emergency situation. For the vast majority of heals, the slower it is, the more mana efficient it is. So, always use slow heals unless you need to quickly top someone off. I realize your question was aimed at Priests but this goes for all healers and almost all heals.