The harsh propagation environment at millimeter-wave (mmW) frequencies can be countered by using large antenna arrays, which can be steered electronically to create directional beams. Knowledge of the key channel characteristics in this environment, including the delay spread, the coherence time, and the coherence bandwidth, plays a significant role in optimal adaptation of the transmission waveform. In this paper, we focus on analyzing the delay spread of a directional mmW channel. A high delay spread causes inter-symbol interference (ISI), which can be mitigated by concatenating cyclic prefixes (CPs) to data symbols at the expense of lower spectral efficiency. Considering a single mmW link, whose transmitter (Tx) and receiver (Rx) are equipped with uniform planar arrays (UPAs), we study the impact of various beamforming attributes (e.g., antenna-array size, beamwidth, beam direction, and beam misalignment) on the average and root-mean-square delay spread. We use detailed simulations with accurate 3GPP channel models and conduct extensive experiments using a 4\times 8 UPA at 28 GHz to verify our analysis. Based on this analysis, we study the optimal beamforming configuration at the Rx for a given Tx beamformer so as to maximize the spectral efficiency. Our proposed beam selection method finds the best Rx beam direction that results in a low delay spread and high signal-to-noise ratio (SNR). Our extensive simulation and experimental results verify that this method significantly improves the spectral efficiency, almost doubling the data rate in some cases.