Adarsh Kumar Dash, Dominic Anstey, Harry T. J. Bevins, Eloy de Lera Acedo, Gary Allen, Kaan Artuc, Gianni Bernardi, Martin Bucher, Steve Carey, Jean Cavillot, Ricardo Chiello, Adelicia S. Chu, Wessel Croukamp, John Cumner, Saswata Dasgupta, Dirk I. L. de Villiers, Jiten Dhandha, Aleksandra Dragovic, John A. Ely, Anastasia Fialkov, Thomas Gessey-Jones, Will J. Handley, Christian Kirkham, Girish Kulkarni, Samuel A. K. Leeney, Alessio Magro, P. Daan Meerburg, Shikhar Mittal, Daniel Molnar, Rohan S. Patel, Joe H. N. Pattison, Saurabh Pegwal, Carla M. Pieterse, Jonathan R. Pritchard, Gabriella Rajpoot, Nima Razavi-Ghods, Daniel Robins, Ian L. V. Roque, Anchal Saxena, Killian H. Scheutwinkel, Emma Shen, Peter H. Sims, Marta Spinelli, Jiacong Zhu

The spin-flip 21-cm signal from the Cosmic Dawn and the Epoch of Reionization is an essential probe of the conditions that led to the formation of the first luminous objects in the early Universe. However, its detection remains a major challenge owing to its low strength compared to the bright foregrounds and the requirement of precise calibration of the instrument to prevent systematics that could hinder a detection or lead to false inferences. REACH (Radio Experiment for the Analysis of Cosmic Hydrogen) is a radiometer experiment designed to detect this sky-averaged signal in the frequency range of 50--130~MHz. Using a wide-beam antenna, REACH calibration relies on internal reference sources, covering a broad range of temperatures and reflection coefficients. The choice of type and number of calibrators used significantly influences the quality of the calibration. This work investigates these effects and introduces a novel method for selecting an optimal set of calibration sources. With an optimised set, we aim to reduce calibration time, thereby increasing sky integration time while preserving calibration accuracy. We explore two optimisation strategies: one applied across the full receiver band and another performed on a frequency-by-frequency basis. Finally, we demonstrate that, with a total calibration time comparable to the conventional full-calibrator set, an optimised set with fewer calibrators achieves approximately a $15~\%$ reduction in calibrated temperature noise and improved absolute calibration of the instrument. This has implications for better calibration strategies in similar radiometer experiments.