Synoptic measurements of activity in Sun-like stars have been performed continuously since 1966, and the largest set comes from the Mount Wilson HK project, in the form of the well-known S index. We have been monitoring the activity and variability of the Sun and a large sample of Sun-like stars, in terms of S and absolute flux, since 1994 with the Solar-Stellar Spectrograph (SSS) at Lowell Observatory. Directly inspired by the similar long-term program at Mount Wilson Observatory, the SSS incorporates both an HK spectrograph and an echelle for visible and far-red observations. This is the first of three papers presenting the results of some 20,000 observations of the Sun and Sun-like stars with the SSS. In this paper we describe our program, review the calibration of solar and stellar fluxes to S and the chromospheric emission fraction R'_HK, compare our derived stellar activity measures to those from other programs, and discuss the broad characteristics of the activity and variability in our target set, with particular attention to good solar analogs and noncycling stars. In subsequent papers we will discuss the echelle data and present detailed examinations of stars of particular interest.