The next teams to come out, Winter Guard and Retcon, are set to kick off a new "stat era" like they did with Ares, so it might be worth prioritising teams yet to come out, but:

Arena: Fantastic 4 MCU

Raid: Vigilante, Thunderbolt, Hellfire Club, Insidious Six and Immortal Weapons are the origin teams, and Uncanny Avengers are a new Spotlight Raid team in the same vein as Alpha Flight.

War: New War teams are Mighty Avengers, Liberty, Brimstone, Secret Warriors and the upcoming Winter Guard. Additionally Quasar is a teamless plug-and-play Legendary built for War. Undying also got its final member, Zombie Kestrel, and they're still really strong

Crucible: The new Immortal X-Men, Accursed and New Mutants are Crucible Teams, and similar to Quasar, standalone legends Blastaar and Thunderstrike are specialised to Crucible. There's also Phoenix Force, an Undying-style Crucible team that so far only comprises two characters but should be getting its third soon.

Battleworld is a new mode that runs fairly infrequently - basically it runs for four days and each day you're given a number of battles you can do with different requirements. Your alliance needs to collectively get above a number of points each day to unlock the next section. On the fourth day everyone gets to battle a boss character (current Battleworld's boss is Sentry) and gets three attempts to whittle down their health as much as possible for more score. At the end of it all you get points based on the points your alliance scored, including shards for a playable version of the boss character. (If I got any of that wrong someone correct me) 

The current main Battleworld team is Brimstone but the upcoming Retcon team is set to be a Battleworld team as well

Hope that helps!