When I am teaching or making recommendations for a two player game (or a solo player) my standard go to is to pick the Arcanist and Exorcist.
Neither is powerful in attacks to start, but they are better on defense for the first time setting. For the Arcanist, I suggest the Seeker Focus, because the Dark/Light Aura is extremely helpful for the new player, especially in those early skirmishes. For the Exorcist I suggest the Sanctifier Focus. Moreover, as you are playing in a co-op, I recommend having the players (if there are two of them) pool their resources at the earliest opportunity to “hire” a mercenary or animal companion if they haven’t found one at that time for the Exorcist. This is my second purchase only to bandages in early game play.
Finally, rather than randomly selection, I suggest (first time only!) that they players select the Arcane Ward Ritual card for the Arcanist, and the Boundless Faith Prayer card for the Exorcist. They are more defensive in ability, and again, will help in that early story game experience. Of course, after this first time I recommend that you randomly select any others as the rules dictate.
With these few adjustments it is a smoother game start more often, and allows the player(s) the chance to level up and get more experience in game play before being clobbered.
What is your ideal solo/small party set up?