Many models of physics beyond the Standard Model predict a strong first-order phase transition (SFOPT) in the early Universe that leads to observable gravitational waves (GWs). In this paper, we propose a novel method for presenting and comparing the GW signals that are predicted by different models. Our approach is based on the observation that the GW signal has an approximately model-independent spectral shape. This allows us to represent it solely in terms of a finite number of observables, that is, a set of peak amplitudes and peak frequencies. As an example, we consider the GW signal in the real-scalar-singlet extension of the Standard Model (xSM). We construct the signal region of the xSM in the space of observables and show how it will be probed by future space-borne interferometers. Our analysis results in sensitivity plots that are reminiscent of similar plots that are typically shown for dark-matter direct-detection experiments, but which are novel in the context of GWs from a SFOPT. These plots set the stage for a systematic model comparison, the exploration of underlying model-parameter dependencies, and the construction of distribution functions in the space of observables. In our plots, the experimental sensitivities of future searches for a stochastic GW signal are indicated by peak-integrated sensitivity curves. A detailed discussion of these curves, including fit functions, is contained in a companion paper [2002.04615]. The data and code that we used in our analysis can be downloaded from Zenodo [https://doi.org/10.5281/zenodo.3699415].
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