This is the first in a series of papers in which we analyze medium-resolution spectra of over 400 K and M giants in Baade's Window. Our sample was selected from the proper motion study of Spaenhauer et al. [AJ, 103, 297 (1992)]. We have measured radial velocities for most of the sample, as well as line-strength indices on the system of Faber et al. [ApJS, 57, 711 (1985)]. We analyze the random and systematic errors in velocities and line strengths, and show that the bright (V < 16.0) stars in our sample are predominantly foreground disk stars along the line of sight toward Baade's Window. We find that most of the bulge K giants have stronger Mg absorption at a given color than do stars in the solar neighborhood. If the K giants in our sample are moderately old, we suggest that on average they may have [Mg/Fe] approximate to +0.3, consistent with the results of recent high-resolution spectroscopy in Baade's Window. (C) 1995 American Astronomical Society.