  Observations of low-frequency gravitational waves will require the highest
possible timing precision from an array of the most spin-stable pulsars. We can
improve the sensitivity of a pulsar timing array (PTA) to different
gravitational-wave sources by observing pulsars with low timing noise over
years to decades and distributed across the sky. We discuss observing
strategies for a PTA focused on a stochastic gravitational-wave background such
as from unresolved supermassive black hole binaries as well as focused on
single continuous-wave sources. First we describe the method to calculate a
PTA's sensitivity to different gravitational-wave-source classes. We then apply
our method to the 45 pulsars presented in the North American Nanohertz
Observatory for Gravitational Waves (NANOGrav) 11-year data set. For expected
amplitudes of the stochastic background, we find that all pulsars contribute
significantly over the timescale of decades; the exception is for very
pessimistic values of the stochastic background amplitude. For individual
single sources, we find that a number of pulsars contribute to the sensitivity
of a given source but that which pulsars contribute are different depending on
the source, or versus an all-sky metric. Our results seem robust to the
presence of temporally-correlated red noise in pulsar arrival times. It is
critical to obtain more robust pulsar-noise parameters as they heavily affect
our results. Our results show that it is also imperative to locate and time as
many high-precision pulsars as possible, as quickly as possible, to maximize
the sensitivity of next-generation PTA detectors.
