I have Some High-Pitched Theroys of why they chose the OLD sumons they did:

Ifrit: A familier and Basic Aeon/summon to get you ready

Shiva: So the Girls on't complain

Bahamut: another Familier face. Although even though he's a cool summon he is begining to look overused......

Still no Explanation for lack of water Aeon though!

Oh and Bahamut was a fish in Mythology