This is a complex question and you are thinking in the right direction. You are correct that to test how different timbres behave in a resonator, you could use different musical instruments to play the same frequency (you could use a digital tuner to match the frequency exactly). However, you always have to ask what factors other than timbre might affect your measurement, so that you can be sure that you are truly measuring the effect of timbre rather than something else.

When you design an experiment, you have to think of as many confounding factors as you can, and either account for them in your experimental design, or just keep track of them as possible sources of uncertainty and error. In science, it is impossible to get rid of uncertainty completely, so we just try to make sure that the error is not big enough to change the final conclusion of the experiment.

For example, in your measurement, different instruments will produce sound at varying volumes and varying degrees of sustain - with a wind instrument, you can maintain the same volume for a while, whereas with a piano or guitar, you can only pluck a note once and let the volume decay. It would be difficult to compare the resonance between a piano and a flute, because the duration of the sound would be completely different. However, if you can pick several musical instruments that can sustain a note for a while at a constant volume, you can do a fair comparison between them and see how the sound resonates in your glass.

Another factor is that some instruments can produce different timbres depending on how they are played, even for the same note. To precisely describe how different overtones resonate, you would need to go from qualitatively describing the timbre as shrill, deep, or some other way, to quantitatively measuring the specific overtones that show up. Of course, measuring the exact overtones can be difficult without special equipment, and not absolutely necessary - it is just important to remember that timbre can change even within a single instrument and this variation is a potential uncertainty in your experiment.