Our previous work in the field of formalization, modeling, and design of adaptive training complexes (ATCs) revealed the low accuracy of the traditional expert approach to selecting ATC components. The study addresses the practical scientific problem of classifying and selecting visualization tools and technologies for designing ATC. Currently, this is done using highly subjective expert evaluation. Therefore, we develop a methodology for the selection of visualization tools and technologies to reduce the influence of the human factor by applying a set of main criteria for visualization component evaluation. Classification is based on the facet approach. We create an original technique that allows users to formalize the main objects of a technical system needing a training complex. It allows users to correlate these aspects to the visualization components and to group, evaluate, and rank them. Integration time, use-cost and component visualization quality, training quality, and time are important variables in the methodology. The use of lexicographic optimization methods or linear convolution of criteria is proposed to obtain an optimal solution from the final Pareto-set. The proposed component selection method has several advantages, compared with the classical approach: greater objectivity of the obtained estimates, better development, and further software implementation automation. Thus, this method addressed the problem of choosing the components of ATC visualization. The significance of the study is in the development of the original algorithmic and mathematical software for the method of selecting ATC visualization components.