We present high-resolution optical (CCD) spectra of 53 T Tauri stars as part of a program to study the emission-line properties of young stars. We interpret the permitted lines in terms of active stellar chromospheres, which emit narrow (less than or similar 40 km s-1) fines (e.g., of Si I, Ca I and II, Mg I and II, and Fe I and II), and extended turbulent envelopes, which produce the usual broad (greater than or similar to 100 km s-1) line profiles. A weak correlation between the H-alpha and narrow-line strengths suggests that these two regions are somehow interacting. In a subsequent paper we estimate that the chromospherically active regions can occupy more than half of the stellar surface, but are usually much smaller. The narrow line widths constrain the velocities to less than or similar 10 km s-1 in the deep chromosphere and less than or similar 22 km s-1 higher up where the He i and ii lines form. This velocity structure is incompatible with models of T Tauri winds driven by the star. Also, the presence of similar active chromospheres in both weak and strong H-alpha sources suggests that the stars beneath the envelopes are roughly the same in all cases. We therefore conclude that the extended high-velocity envelopes have a nonstellar origin and a nonspherical geometry. We favor a model in which the envelope forms at a star-accretion disk boundary layer and resides primarily near the disk plane. Examination of the broad Ca II triplet lines indicates that the inner high-velocity envelopes have minimum space and column densities of n(e) approximately 10(11) cm-3 and N(H) approximately 10(21) (V(turb) 50 km s-1) cm-2, respectively, where V(turb) is the local Doppler velocity. The broad triplet emitting regions are sometimes several times larger than the stars, but can also be much smaller. We interpret the smooth single-peaked triplet profiles, and the broad stationary O I lambda-7773 absorptions (in three sources), as evidence for large turbulent velocities (greater than or similar to 50 km s-1) in the inner envelope. These velocities decrease (inward?) by approximately 20 to 50% between the regions where H-alpha and the Ca II triplet are emitted. Direct evidence for outflow or infall appears only rarely in the form of velocity shifted absorption lines. Blueshifted permitted emission lines (e.g., in S CrA) are detected as a rare and transient phenomenon. A trend appears in about half of the objects measured for the weakest transition in the Ca II triplet, 8498 angstrom, to have the largest peak height and smallest width. We attribute this to the combined effects of an outward rise in the turbulent velocities and a rapid decline (and perhaps inversion) of the triplet source function.