This paper presents the results of experiments conducted on a batch of additively manufactured customized prosthetic sockets for upper limbs, made of thermoplastics and designed automatically on the basis of a 3D-scanned limb of a 3-year-old patient. The aim of this work was to compare sockets made of two different materials—rigid PLA and elastic TPE. Two distinct socket designs with various mounting systems were prepared. To find a reliable set of parameters for cheap and stable manufacturing of usable prostheses using 3D printers, realizing the fused deposition modeling (FDM) process, sets of sockets were manufactured with various process parameters. This paper presents the methodology of the design, the plan of the experiments and the obtained results in terms of process stability, fit and assessment by patient, as well as strength of the obtained sockets and their measured surface roughness. The results are promising, as most of the obtained products fulfil the strength criteria, although not all of them meet the fitting and use comfort criteria. As a result, recommendations of materials and process parameters were determined. These parameters were included in a prototype of the automated design and production system developed by the authors, and prostheses for several other patients were manufactured.