The Thousand Pulsar Array (TPA) project currently monitors about 500 pulsars with the sensitive MeerKAT radio telescope by using subarrays to observe multiple sources simultaneously. Here we define the adopted observing strategy, which guarantees that each target is observed long enough to obtain a high fidelity pulse profile, thereby reaching a sufficient precision of a simple pulse shape parameter. This precision is estimated from the contribution of the system noise of the telescope, and the pulse-to-pulse variability of each pulsar, which we quantify under some simplifying assumptions. We test the assumptions and choice of model parameters using data from the MeerKAT 64-dish array, Lovell and Parkes telescopes. We demonstrate that the observing times derived from our method produce high fidelity pulse profiles that meet the needs of the TPA in studying pulse shape variability and pulsar timing. Our method can also be used to compare strategies for observing large numbers of pulsars with telescopes capable of forming multiple subarray configurations. We find that using two 32-dish MeerKAT subarrays is the most efficient strategy for the TPA project. We also find that the ability to observe in different array configurations will become increasingly important for large observing programmes using the Square Kilometre Array telescope.