Personally, I prefer using the Batarian Sentinel with Subnet maxed against Cerberus, with a gun like Falcon or Venom. The stagger gives you a lot of breathing space, you can punch many of the enemies and the Subnet is a good form of crowd control, snatching Phantoms like nothing, with the help of the forementioned stagger, of course. The Asari Adept is also good, as well as the Volus Adept with Stasis and immediate BE with his Biotic Balls, but, for me, the Batarian Sentinel is my favourite, because he is buff.
As of late, I prefer using the Talon Mercenary against Collectors. His moves pack a kick and if I remember correctly, he's not affected by the Swarms and even if he is, even a naked Omni-bow can do the trick with mooks. I also like the Batarian Soldier for the same reason. He only has on CD dependent move and that is only for emergencies that require stagger.
Aside from the Paladin, I will gladly use the Salarian Engineer, the Human Engineer and the Volus Mercenary against Geth. The SE uses the Decoy and attacks from range, so he won't get too close for comfort, as long as you keep an eye out for Hunters. The Volus Merc makes Geth hilarious. The HE follows the same logic. Just use your toys, people.
For Reapers... Krogan Soldier, N7 Demolisher and Cabal Vanguard are my go-to kits. The Cabal Vanguard is good at finding an escape route if needed and the Krogan Soldier is well, the Krogan Soldier. Fire. Everywhere. As for the N7 Demolisher... Well, just kill a Cannibal, wait for the other Cannibals to go for lunch, launch a Homing on them. She may depend on grenades to work, but if she has them, boy, does she work.
But my All-Faction-Favourite is the Asari Valkyrie. Play her correctly and she will make every match feel like a dream. She's fast, powerful, efficient and she has just enough of bulk to allow you to escape some bad stuff.