Pretty interesting question, honestly it's a little difficult to tell with all the trailers and gameplay footage with dev builds that showcase different Eikons at different "Levels" and events.

My guess would be:

1. Phoenix - Obviously
2. Garuda - Clive and Cid both being shocked that he absored Benedikta's essence/mana in the Gameplay footage we got from the Media Tour) (Probably a smaller mission after being brought to the Hideaway by Cid.)
3. Ramuh - Cid will volunteer to train Clive to control his Eikon abilities after the encounter with Benedikta/Garuda and finding out that Clive transforms into Ifrit, and as a result lend him Ramuh.
4. Shiva - Jill was no-where in the Garuda/Lost Keep footage/gameplay we saw in the Media Tour, possibly because the dev's hid it and built that Media Tour differently from the game or because as per the story, she's knocked out and healing after being saved and brough to the Hideaway following the Titan vs Shiva fight.
5. Titan - Seems to be the next possibly target, we see Clive in the newer "Red Gear" in every fight with Titan but still in the Grey "Sanbreque" outfit against Garuda in the Media Tour.
6. Odin - To be honest, not sure. May as well be tied with Bahamut
7. Bahamut - As mentioned above, not really sure but because Bahamut is usually the strongest, if not last Summons in the franchise.