I was wondering if there is a logic to the order you make the offerings to the statues in the shrines. I have the impression that if you make the offerings in a specific order, the results should be more or less rewarding.

Considering there's no guarantee you'll even be able to make two of the sacrifices (i.e., the required amount of the health and mana offerings are determined as a certain percentage of your current max for those values, and if your current total in whatever resource is lower than that required value, you won't be allowed to make that sacrifice), I seriously doubt that that's the case. Anyway, I haven't seen anything that would seem to indicate that.