Let’s see

III - I’ve honestly never used summons here lol
IV - the Mist Dragon is cool if only for its personal connection with the summoner. Plus the design is pretty
V - Carbuncle. It really comes in handy and I love the contrast between his angry form you battle and the cute critter you summon
VI - a lot to choose from, but I think I’d pick Alexander, as it definitely has my favorite design here
VII - Choco/Mog, actually, just for having a funny animation
VIII - this game has some of the coolest designs imo. But I think my vote goes to newcomer Diabolos
IX - Fenrir, based purely on aesthetics tbh
X - Anima for being hilariously out of place
XII - I think Hashmal will get my vote here, but I think the Ivalice summons were just awesome overall
XIII - Odin, probably, though he’s far from the coolest incarnation
XV - Either Ramuh or Shiva. The former for being unbelievably epic in proportions, really making him far more badass than just an old dude with a staff has any right to be, and the latter for the story involvement and there being so many of her