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The NIRCam instrument on the upcoming James Webb Space Telescope (JWST) will offer an unprecedented view of the most distant galaxies. In preparation for future deep NIRCam extragalactic surveys, it is crucial to understand the color selection of high-redshift galaxies using the Lyman dropout technique. To that end, we have used the JAdes extraGalactic Ultradeep Artificial Realizations (JAGUAR) mock catalog to simulate a series of extragalactic surveys with realistic noise estimates. This enables us to explore different color selections and their impact on the number density of recovered high-redshift galaxies and lower-redshift interlopers. We explore how survey depth, detection signal-to-noise ratio, color selection method, detection filter choice, and the presence of the Ly$\alpha$ emission line affects the resulting dropout selected samples. We find that redder selection colors reduce the number of recovered high-redshift galaxies, but the overall accuracy of the final sample is higher. In addition, we find that methods that utilize two or three color cuts have higher accuracy because of their ability to select against low-redshift quiescent and faint dusty interloper galaxies. We also explore the near-IR colors of brown dwarfs and demonstrate that, while they are predicted to have low on-sky densities, they are most likely to be recovered in F090W dropout selection, but there are color cuts which help to mitigate this contamination. Overall, our results provide NIRCam selection methods to aid in the creation of large, pure samples of ultra high-redshift galaxies from photometry alone., Comment: 24 pages, 20 figures, accepted for publication in the Astrophysical Journal