If I recall, whilst the gender the egg itself hatches into is random, there is a pattern. I read it when wave 1 came out from a user here so can't remember which egg is which but:
Egg 1: Boy/Girl/Boy/Girl etc or vice versa
Egg 2: 3 Boys/3 Girls/3 Boys etc or vice versa
Egg 3: Completely random
I don't know how correct that theory is or how it changes if two Friends breed.
Otherwise nothing is affected by egg choice.