Damping constant for maximum response in resonant systems

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Given a system where a damped spring has natural frequency equal to the frequency of the input oscillations, how do I choose a damping constant in order to maximize the response of the spring?

Are there any issues with choosing a zero damping constant? (as this would surely provide the maximum response even if it does mean it oscillates forever in the absence of friction)

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The "maximum" response is generally with 0 damping. I see no problem with using that.
 
Theoretically, there's no issue with choosing a zero damping constant. Simple harmonic motion is described by a spring with no damping constant. Of course, for real world applications, it's always a factor.