Hyde/Orie is currently my most stable team.
I originally wanted to run Hyde/Hazama, but neutral is very very VERY important in BBTAG, and Hazama being able to skip neutral entirely will probably only lead to me developing worse habits as a player if I kept playing him while I'm still learning the game.
As such, I'm going with a very neutral-dependent team. Both Hyde and Orie are very stable solo, and both have access to great assists. (Hyde in particular has some of the best in the game.)
I've also had fun with Hazama/Yosuke, Hyde/Ragna, and Naoto/Hazama.