Cell-free massive MIMO systems consist of many distributed access points with simple components that jointly serve the users. In millimeter wave bands, only a limited set of predetermined beams can be supported. In a network that consolidates these technologies, downlink analog beam selection stands as a challenging task for the network sum-rate maximization. Low-cost digital filters can improve the network sum-rate further. In this work, we propose low-cost joint designs of analog beam selection and digital filters. The proposed joint designs achieve significantly higher sum-rates than the disjoint design benchmark. Supervised machine learning (ML) algorithms can efficiently approximate the input-output mapping functions of the beam selection decisions of the joint designs with low computational complexities. Since the training of ML algorithms is performed off-line, we propose a well-constructed joint design that combines multiple initializations, iterations, and selection features, as well as beam conflict control, i.e., the same beam cannot be used for multiple users. The numerical results indicate that ML algorithms can retain 99-100% of the original sum-rate results achieved by the proposed well-constructed designs.