We present optical spectra and photometry sampling the first 6 months after discovery of supernova (SN) 1999gi in NGC 3184. SN 1999gi is shown to be a Type II-plateau event with a photometric plateau lasting until about 100 days after discovery. Using the expanding photosphere method (EPM), we derive a distance to SN 1999gi of 11.1 Mpc and an explosion date of 1999 December 5.8, or 4.1 days prior to discovery. This distance is consistent with a Tully-Fisher distance recently derived to NGC 3184 (D ≈ 11.59 Mpc), but it is somewhat closer than the Cepheid distances recently derived to two galaxies that have generally been assumed to be associated with the group containing NGC 3184 (NGC 3319, D = 13.30 ± 0.55 Mpc, and NGC 3198, D = 13.80 ± 0.51 Mpc). From many lines of evidence, we conclude that SN 1999gi is only minimally reddened. A comparison between the color of SN 1999gi at early times and that of an infinitely hot blackbody restricts the reddening to E(B-V) < 0.45 mag, while a comparison between the color evolution of SN 1999gi and the well-observed (and extensively modeled) Type II-P SN 1999em implies an even more restrictive upper reddening limit of E(B-V) < 0.3 mag. A variety of other, independent reddening estimates are consistent with these upper limits and yield a probable reddening of E(B-V) = 0.21 ± 0.09 mag. We reconsider the upper mass limit (9 M⊙) recently placed on the progenitor star of SN 1999gi by Smartt et al. in light of these results. Following the same procedures, but using the new data presented here, we arrive at a less restrictive upper mass limit of 15 M⊙ for the progenitor. The increased upper limit results mainly from the larger distance derived through the EPM than was assumed by the Smartt et al. analyses, which relied on less precise (and less recent) distance measurements to NGC 3184. Finally, we confirm the existence of "complicated" P Cygni line profiles in early-time and later photospheric-phase spectra of SN 1999gi. These features, first identified by Baron et al. in spectra of SN 1999em as high-velocity absorptions, in addition to the "normal" lower velocity component, are here verified to be true P Cygni profiles consisting of both an absorption trough and an emission peak at early times. In the earliest spectrum, taken less than a day after discovery, the features extend out to nearly -30,000 km s-1, indicating the existence of very high velocity material in the outer envelope of SN 1999gi.