There is no “right” answer here. Which wire you measure depends on how the rest of your model looks. If the model is (i.e., circuit diagram doesn’t change if you relabel&rearrange wires), then it won’t matter which wire you use. You could also measure expectations on both wires and combine them together in a classical cost function.
Regarding categorical output, Fock states are a natural encoding strategy, but I wouldn’t say this choice is obviously favoured over others. This is the kind of choice that is best verified by experiment.