My own preference is for a pure sinewave output, although I have constructed Theremins with features for harmonic selection as well. Some designs, including the ones described by Leon Theremin in his 1929 United States patent, have one or more tone control knobs. In this respect, it is nice to have tonal variation available to provide a variety of sounds in lieu of virtuoso content. Lastly, the subject of noise gives consideration to two primary factors. First, the susceptibility of an instrument to electromagnetic interference, such as that from a radio station, can cause problems manifested in unwanted audible disruptions.
Most units have some sort of tuning provision to selectively eliminate such disturbances.
By definition, this ratio will be at least as large as the volume range, but may exceed this value, which is a benefit. Ambient distractions often make hearing the Theremin difficult, and, under these circumstances, the performer no longer has the feedback vital for control. Good, loud monitors are an asset in this respect, so, if you plan to bring your Theremin to concert, be prepared with the right amplifier and monitor speaker for the occasion. In the studio, headphones with a careful blend of the accompaniment is essential.