Microresonator-based frequency combs (microcombs or Kerr combs) can potentially miniaturize the numerous applications of conventional frequency combs. A priority is the realization of broadband (ideally octave spanning) spectra at detectable repetition rates for comb self-referencing. However, access to these rates involves pumping larger mode volumes and hence higher threshold powers. Moreover, threshold power sets both the scale for power per comb tooth and also the optical pump. Along these lines, it is shown that a class of resonators having surface-loss-limited Q factors can operate over a wide range of repetition rates with minimal variation in threshold power. A new, surface-loss-limited resonator illustrates the idea. Comb generation on mode spacings ranging from 2.6 to 220 GHz with overall low threshold power (as low as 1 mW) is demonstrated. A record number of comb lines for a microcomb (around 1900) is also observed with pump power of 200 mW. The ability to engineer a wide range of repetition rates with these devices is also used to investigate a recently observed mechanism in microcombs associated with dispersion of subcomb offset frequencies. We observe high-coherence phase locking in cases where these offset frequencies are small enough so as to be tuned into coincidence. In these cases, a record-low microcomb phase noise is reported at a level comparable to an open-loop, high-performance microwave oscillator.