I would personaly love to see as many classical summons as possible (like at least one for each element) and also I would love to see their cinematic typical moves (and skip button =D).
Fire Element - Ifrit and Phoenix, who would come with raise/auto-raise effect.
Ice Element - Shiva
Thunder Element - Ramuh or Ixion. I really loved FFX Thunder summon, so if they would put him back, it would be fine with me.
Earth Element - Titan, since he's confirmed.
Water Element - Leviathan, the same as Titan.
Wind Element - I've got a problem with this one, since I'm not sure if FF series have any classical wind summon. Also I don't like Pandemona. I would probably go with Valefor even though it's not wind elemental summon.
Gravity Summon - I would choose Atomos, because...
Dark Summon - ...because I would like to see Diabolos to be made as dark summon. I mean he looks so badass and evil, he should be on the dark side =D
Light Summon - Alexander, because I love him and because he is my the most favourite summon. I just hope they would make him really huge and epic, with angelic wings (FF IX-like)
Status Summon - Hades or Doomtrain. Also I would like to see Siren, because I'm sure she would be hot!
Non-Elemental Summon - without questions, Bahamut, maybe more versions of him. I would also like to see Fenrir be made offensive, in which case he would probably be in this category. Or in wind category, not sure. Also, Odin goes without question. Moreover I would love to see some new ultimate summon, who would be also non-elemental.
Buff Summon - I want see summons like Golem, Unicorn, Cerberus, Carbuncle and more.
That's it. Also I would like to be able fight all these summons, since I can never get enough of epic fights.