What level of enchantment gives me the best chance for Aqua Affinity or Respiration?

Solution 1:

Actually, you are mistaken. I have run 1 million enchantments for each level from 1 to 30 and counted the number of times I got each particular enchantment. Here are the results for diamond helmet:

You can clearly see that 30 level enchanting gives the maximum chance of getting Respiration or Aqua Affinity.

Running the same test for a golden helmet (which has better enchantability) gives almost the same picture - Aqua affinity actually peaks on level 28, but Respiration III is rising significantly on levels 29 and 30, so still a better strategy is to enchant on level 30:

Here is the raw data including all diamond helmet enchantments if you'd like to play around with it. I have used MCP 9.03 (Minecraft 1.7.2) to generate the results, but I'm not aware of any changes in the enchantment probabilities since then. Even in the upcoming 1.8 where the enchanting mechanic is changed, the probabilities and enchantment selection were not changed (according to Jeb). It is possible however that the enchanting will be revisited once more before the final 1.8 release.

I guess I could include the book enchantment probabilities for completeness, but they are lower than the helmet ones by an order of magnitude: