Automated selection of the best-performing algorithm for a given optimisation problem is crucial. However, how effectively automated algorithm selectors perform on problem classes beyond their training set remains an open area of investigation. While prior research has examined the impact of different problem representations and benchmarking suites on the ability of selectors to perform well on unseen problem classes, the influence of optimisation algorithm portfolio composition and machine learning model choice remains underexplored. This study investigates how these factors influence cross-benchmark performance of selectors in single-objective black-box optimisation. Problem instances are generated from two distinct benchmarking suites, i.e., the Black-Box Optimisation Benchmarking (BBOB) and Sinha-Malo-Deb (SMD), and represented using Exploratory Landscape Analysis features. Ninety-nine portfolios, each containing three to seven optimisation algorithms, and six machine learning models are evaluated under a train-on-BBOB and test-on-SMD scenario. The results show that portfolio composition strongly influences both Oracle-Baseline performance gap (the difference between the performance of an ideal selector and a baseline selector) and portfolio complementarity (how well algorithms within a portfolio complement each other). These factors, in turn, govern the ability of selectors to generalise beyond their training problem set. Furthermore, the choice of machine learning model can substantially affect how much of Oracle-Baseline performance gap is closed. Moreover, some machine learning models leverage portfolio complementarity more effectively to perform well across benchmarking suites. These findings highlight that careful selection of optimisation algorithms within a portfolio, combined with appropriate machine learning models, is key to robust automated algorithm selection.