In this paper, we statistically analyze the performance of a threshold-based parallel multiple beam selection scheme for a free-space optical (FSO) based system with wavelength division multiplexing (WDM) in cases where a pointing error has occurred under independent identically distributed Gamma-Gamma fading conditions. To simplify the mathematical analysis, we additionally consider Gamma turbulence conditions, which are a good approximation of Gamma-Gamma distribution. Specifically, we statistically analyze the characteristics in operation under conventional detection schemes (i.e., heterodyne detection (HD) and intensity modulation/direct detection (IM/DD) techniques) for both adaptive modulation (AM) case in addition to non-AM case (i.e., coherent/non-coherent binary modulation). Then, based on the statistically derived results, we evaluate the outage probability of a selected beam, the average spectral efficiency (ASE), the average number of selected beams (ANSB) and the average bit error rate (BER). Selected results show that we can obtain higher spectral efficiency and simultaneously reduce the potential for increasing the complexity of implementation caused by applying the selection-based beam selection scheme without considerable performance loss. Especially for the AM case, the ASE can be increased further compared to the non- AM cases. Our derived results based on the Gamma distribution as an approximation of the Gamma-Gamma distribution can be used as approximated performance measure bounds, especially, they may lead to lower bounds on the approximated considered performance measures.