In this paper, we provide a global framework analysis of a dual-hop mixed Radio Frequency (RF)/Free Space Optical (FSO) system with multiple branches/relays wherein the first and second hops, respectively, consist of RF and FSO channels. To cover various cases of fading, we propose generalized channels' models for RF and FSO links that follow the Nakagami-m and the Double Generalized Gamma (DGG) distributions, respectively. Moreover, we suggest Channel State Information (CSI)-assisted relaying or variable relaying gain based Amplifiy-and-Forward (AF) amplification. Partial relay selection with outdated CSI is assumed as a relay selection protocol based on the knowledge of the RF CSI. In order to derive the end-to-end Signal-to-Interference-plus-Noise Ratio (SINR) statistics such as the Cumulative Distribution Function (CDF), the Probability Density Function (PDF), the higher order moments, the amount of fading and the Moment Generating Function (MGF), the numerical values of the fading severity parameters are only valid for integer values. Based on these statistics, we derive closed-forms of the outage probability, the bit error probability, the ergodic capacity and the outage capacity in terms of Meijer-G, univariate, bivariate and trivariate Fox-H functions. Capitalizing on these expressions, we derive the asymptotic high SNR to unpack valuable engineering insights of the system performance. Monte Carlo simulation is used to confirm the analytical expressions.