I'm going to be boring and say the Freedom Five is my go-to team, with whom I rarely, if ever, lose. And I try to do them in order of when they're recruited according to the comic, because I'm a dork.
Legacy -- self explanatory. Up to +2 to all damage, protection, extra cards...honestly, he's the one I leave out when I want a challenge.
Bunker -- he's my main damage dealer, goal is usually to get Flak Cannon or Grenade Launcher out along with the Omnicannon, though occasionally I'll focus him on tanking and healing. I love him in minion-heavy decks. A couple rounds against Voss with Ammo Drop out and I've got damn near his whole deck in my hand.
Tachyon -- she pairs extremely well with Legacy, who turns all her 1-damage cards into serious damage, and having her keep the villain from doing damage for a round is invaluable. She also ends up being another nuker toward the end, though I'll occasionally use Lightspeed Barrage as quick problem solving.
Wraith -- she mainly finds use as deck control -- having one or two Eyepieces out makes most villains outright trivial. Sometimes I'll use her damaging powers (with Legacy buffing everyone +2 and her computer? Scary.), but I find a lot more use for her as a problem solver than a damage dealer.
Absolute Zero -- He benefits the most out of Legacy's buffs, and I can regularly get hugely powerful turns out of him. Plus his ability to heal (again, hugely boosted by Legacy's buffs) makes him as good a tank as anyone despite his lack of armor. He's also amazing for Ongoing destruction.
Sometimes I'll switch out AZ for Unity -- with all her potential instances of damage (plus Champion Bot) she can be insane on a team with Legacy's buffs. If I can keep her bots out for more than a round or two, that usually spells the end of a villain.
I'm really waiting for the IR expansion in the app, though, so I can start playing around with Argent Adept and Nightmist. I've played with them a couple times in the physical game, and I'm itching for a chance to really experiment. Once they do, my go-to team might change.