Horde Mode. Your fire team defeats enemies that comes in waves, and in the final one you get to fight a boss.
Boss Rush Mode. Your fireteam defeats bosses solely.
Competitive. Your fireteam races another fireteam to seek out which team defeats more enemies than other.
Survival Mode. Like Horde Mode, only endless.
I personally think that the Arena mode will be something like a Horde Mode, but a Boss Rush Mode seems plausible too.
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Edited by tatesmus: 4/17/2015 6:28:39 PMI would actually be ok with any of them. I have a heck of a time finding more than three to play with, and rarely get to play for more than an hour or two at a time, so any of the above would be worth it to me.