Isolation and functional characterization of microorganisms are relevant steps for generating starter cultures with functional properties, and more recently, those related to improving mental health. Milk kefir grains have been recently investigated as a source of health-related strains. This study focused on the evaluation of microorganisms from artisanal Mexican milk kefir grains regarding probiotic properties, in vitro fermentability with commercial prebiotics (lactulose, inulin, and citrus pectin), and γ-aminobutyric acid (GABA)-producing capacity. Microorganisms were identified belonging to genera Lactococcus, Lactobacillus, Leuconostoc, and Kluyveromyces. The probiotic properties were assessed by aggregation abilities, antimicrobial activity, antibiotic susceptibility, and resistance to in vitro gastrointestinal digestion, showing a good performance compared with commercial probiotics. Most of isolates maintained a concentration above 6 log colony forming units/mL after the intestinal phase. Specific isolates of Kluyveromyces (BIOTEC009 and BIOTEC010), Leuconostoc (BIOTEC011 and BIOTEC012), and Lactobacillus (BIOTEC014 and BIOTEC15) showed a high fermentability in media supplemented with commercial prebiotics. The capacity to produce GABA was classified as medium for L. lactis BIOTEC006, BIOTEC007, and BIOTEC008; K. lactis BIOTEC009; L. pseudomesenteroides BIOTEC012; and L. kefiri BIOTEC014, and comparable to that obtained for commercial probiotics. Finally, a multivariate approach was performed, allowing the grouping of 2–5 clusters of microorganisms that could be further considered new promising cultures for functional dairy food applications.