How do I select an appropriate controller gain for this roll control autopilot?
You want fast response, but not any overshoot. The perfect response to a step input in this case would be a critically damped one. Matlab/Simulink are your friends here.

Things to consider in your feedback loop:


Aircraft dynamics - is the initial inertia response modelled? Meaning, does the aircraft roll spool up to its final roll rate upon aileron deflection?
Is aerodynamic resistance to roll modelled?
Is it a digital loop, and if so what integrators are you using? If Euler your loop rates need to be high.


I've seen a similar design for a helicopter with a controller gain of 20 and an additional roll compensator $\frac {s + 1}{s}$ in the forward loop, and a negative unity feedback.

You could eyeball the response, use different settings for the feedback gain, and find the fastest response without overshoot. You'd have to testcase it for several extremes. You do need some form of damping feedback as well, I reckon your first task would be to find a response that is not oscillating.