  The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a
computationally expensive complex analysis that involves source-specific noise
studies. As more pulsars are added to the arrays, this stage of PTA analysis
will become increasingly challenging. Therefore, optimizing the number of
included pulsars is crucial to reduce the computational burden of data
analysis. Here, we present a suite of methods to rank pulsars for use within
the scope of PTA analysis. First, we use the maximization of the
signal-to-noise ratio as a proxy to select pulsars. With this method, we target
the detection of stochastic and continuous gravitational wave signals. Next, we
present a ranking that minimizes the coupling between spatial correlation
signatures, namely monopolar, dipolar, and Hellings & Downs correlations.
Finally, we also explore how to combine these two methods. We test these
approaches against mock data using frequentist and Bayesian hypothesis testing.
For equal-noise pulsars, we find that an optimal selection leads to an increase
in the log-Bayes factor two times steeper than a random selection for the
hypothesis test of a gravitational wave background versus a common uncorrelated
red noise process. For the same test but for a realistic EPTA dataset, a subset
of 25 pulsars selected out of 40 can provide a log-likelihood ratio that is
$89\%$ of the total, implying that an optimally selected subset of pulsars can
yield results comparable to those obtained from the whole array. We expect
these selection methods to play a crucial role in future PTA data combinations.
