For now, we have :

Primordial Primal : Bahamut

Cute Primal : Evil Moogle

Elemental Primals :

Titan
Ifrit
Leviathan
Garuda
(Ramuh or Ixion)
(Shiva or ???)

Odin : Nothing is known about him but he was not annonced to be neither a Primal nor a Avatar

Avatars : Carbuncle

List of some Common Final fantasy Summons:

Diabolos
Fenrir
Alexander
Phoenix
Ixion
Valefor
Siren\Ondine
Gilgamesh
Atomos

Cerberus
Maduin
Anima
Yojimbo
Brynhildr
Hecatoncheir
Golem
Quetzacoalt
Pandemona (zephir)
Eden \ Ark
Magus sisters
Kujata
Bismarck
Asura
Hydra
Hades
Kirin
Seraph
Valigarmanda
Pandemona
Typhoon
Doomtrain

Knight of the Rounds : OMGs O_O
12 Zodiacal Summon of Ivalice

Now if we go with the idea that it may have elemental avatar, Which will you choose ?

Fire : Phoenix
Ice : ??? or Fenrir
Lightning : Ixion
Water : Siren or ???
Earth : Hecatoncheir or Golem
Wind : ?????

But at the end whatever they choose it will be cool