I think the extra class will be a sort of engineer guy. Maybe he can also hack some robots or control panels and stuff for various helpful effects. And he has this cool drone to do recon and flush enemies out of cover.
Then we have: Ranger, Sniper, Assault, Engineer, Support.
I'm merging heavy with assault. He's the guy capable of all-out offense if needed, but with a chance for collateral damage. I think the ranger will be handling short-range combat anyways, what with the sword and stuff. And he can use stealthy entry techniques instead of breaching like XCOM1 assaults.
Storywise, I'm expecting the enemy of the aliens to show up. Teaming up with aliens possible. Maybe it'll be the volunteer who eventually overrides control of aliens after merging with an ethereal or the alien hive mind while sacrificing himself.
Also, it's terribly easy for the aliens to have won. XCOM is likely to have lost a few countries to panic, where the aliens could easily take over with some mind control and brainwashing. Let's not forget how easily religions and extremist ideals spread in crises. I doubt much manipulation is needed to make it seem like the aliens were trying to be beneficial. Plus, it's likely that alien tech, after spreading post-resistance, had a roll in the alien coup.
The seperate alien force arriving and seeming beneficial is a possibility as well. "Look, THEY stopped the previous alien force, let's celebrate 'em!" I mean, aliens were reported in the news, but XCOM remained undercover as much as they could.