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In this paper, we develop analytical tools for the performance analysis of coded, coherent communication systems on independent and identically distributed Nakagami-m fading channels with selection combining (SC) diversity. First, we derive an exact expression for the moment generation function (MGF) of the signal-to-noise ratio (SNR) of a code symbol at the output of the selection combiner. Next, based on Gauss-Chebyshev quadrature and Gauss-Laguerre quadrature rules, we propose a simple to compute, yet accurate, numerical solution for the pairwise error probability (PEP) of coded M-phase-shift keying (PSK) signals. Using the PEP expressions, we present the union bound-based bit-error performance of trellis-coded modulation schemes and turbo codes. Finally, we derive an exact expression for the computational cutoff rate of a coded system with M-PSK signaling and SC diversity, and show that the cutoff rate expression is a simple function of the MGF of the SNR at the output of the diversity combiner.