I want to know what game modes there available (right now, not coming up) to play in an offline set-up. Can you play the story mode in co-op, or only online multiplayer?
Currently, you can only play Balloon Fight in the 1v1 local multiplayer. You can not do co-op story mode. Online multiplayer has two modes, Turf Wars and Splat Zones (a.k.a. ranked mode), the latter of which unlocks once you reach level 10.