Metal-organic frameworks (MOFs) hold significant potential for applications that require precise chemical patterning, such as desalination and atmospheric water harvesting. However, many MOFs exhibit poor stability in water. Alongside water stability, a high capacity for water uptake at ambient conditions is anticipated to be essential for the practical use of MOFs in water-related applications, prompting a large-scale computational search. In this study, we employ a combination of machine learning and high-throughput screening methods to identify water-stable MOFs with substantial water uptake capabilities. Using a subset of previously curated MOFs known to have exceptionally high water stability, we investigate the impact of linker functionalization with twelve diverse hydrophilic functional groups, which are expected to enhance water uptake further. For these 736 MOFs, we utilize grand canonical Monte Carlo (GCMC) simulations to calculate their water uptake potential. We find strong positive correlations between pore characteristics of the MOFs, such as the largest cavity diameter and volumetric pore volume, and their water uptake capacity. This relationship breaks down, however, in MOFs featuring extremely hydrophobic linkers that repel water molecules, leading to low water uptake even for these MOFs with large pores. Lastly, we create machine learning models to concurrently screen new MOFs for both water stability and water uptake capacity. From a collection of hypothetical and experimental MOFs, we identify 74 promising materials that are predicted to be both water-stable and capable of high water uptake, all within the applicability range of the machine learning models.