I've noticed a bunch of people on the server have been asking around what the best level to enchant at is for specific enchants. I've done a little math and I've found the best lvl:odds ratio for some sought after enchants.
Also, these odds are the same regardless of what mat the item is made out of, unless otherwise specified.
Silk Touch - lvl 33 with a 5.56% chance
Flame Bow - lvl 26 with a 13.33% chance.
Infinity Bow - lvl 26 with a 6.67% chance.
Fortune III - lvl 50 with a 6.60% chance on a diamond pick.
Sharpness V - lvl 50 with a 9.8% chance on a diamond sword.
Aqua Affinity - lvl 1 with an 11.02% chance on a diamond helmet.
Note: while the odds for landing AA are highest at lvl 1, the chance for multiple enchants is quite low. Your odds are inversely proportional to the enchant level up until about lvl 13, where it stays constant until lvl 32 [7.69%], but the odds of better second or third enchants increases. This is ignoring the chance of AA being the second or third (or even fourth) enchant.
Respiration III - lvl 39 with an 8.22% chance.
Fire Aspect II - lvl 39 with a 6.90% chance.
Feather Falling IV - lvl 30 with an 18.52% chance.
If you'd like to see the best lvl for different Enchants, or even the odds for an enchant at a certain level, just leave a reply, and be sure to leave the material the item is made of.