Touchscreen-based systems are growing in popularity as a tractable, translational approach for studying learning and cognition in rodents. However, while mouse strains are well known to differ in learning across various settings, performance variation between strains in touchscreen learning has not been well described. The selection of appropriate genetic strains and backgrounds is critical to the design of touchscreen-based studies and provides a basis for elucidating genetic factors moderating behavior. Here we provide a quantitative foundation for visual discrimination and reversal learning using touchscreen assays across a total of 35 genotypes. We found significant differences in operant performance and learning, including faster reversal learning in DBA/2J compared to C57BL/6J mice. We then assessed DBA/2J and C57BL/6J for differential sensitivity to an environmental insult by testing for alterations in reversal learning following exposure to repeated swim stress. Stress facilitated reversal learning (selectively during the late stage of reversal) in C57BL/6J, but did not affect learning in DBA/2J. To dissect genetic factors underlying these differences, we phenotyped a family of 27 BXD strains generated by crossing C57BL/6J and DBA/2J. There was marked variation in discrimination, reversal and extinction learning across the BXD strains, suggesting this task may be useful for identifying underlying genetic differences. Moreover, different measures of touchscreen learning were only modestly correlated in the BXD strains, indicating that these processes are comparatively independent at both genetic and phenotypic levels. Finally, we examined the behavioral structure of learning via principal component analysis of the current data, plus an archival dataset, totaling 765 mice. This revealed 5 independent factors suggestive of "reversal learning," "motivation-related late reversal learning," "discrimination learning," "speed to respond," and "motivation during discrimination." Together, these findings provide a valuable reference to inform the choice of strains and genetic backgrounds in future studies using touchscreen-based tasks.