Research on text comprehension in relation to the reading medium (paper or screen) has mainly involved undergraduate or high school students. To advance current knowledge on the effects of reading medium, this longitudinal study focused on beginner readers, specifically, the role of precursors in first graders' comprehension of narrative and expository linear texts from reading on paper and computer screen. Working memory and inference skills as cognitive precursors and basic digital skills were measured at the end of preschool (T1); reading text comprehension and word reading, as a control variable, were measured at the end of the first grade (T2). Sixty-three children participated in total. The first graders read four texts, one narrative and one expository, on both paper and computer screen, in a counterbalanced order. Results showed no main effects of the reading medium or text genre, but the interactive effect of these variables was significant. At T2, the children had higher comprehension scores after reading narrative than descriptive texts from paper. In addition, reading from the screen was preferred at post-test, after all texts were presented. As precursors, working memory and inference skills predicted both printed and digital text comprehension. In contrast, basic digital skills predicted only digital text comprehension after controlling for medium, text genre, and word reading.