We present an investigation of the optical spectra of 264 low-redshift (z<0.2) Type Ia supernovae (SNe Ia) discovered by the Palomar Transient Factory, an untargeted transient survey. We focus on velocity and pseudo-equivalent width measurements of the SiII 4130, 5972, and 6355{AA} lines, as well those of the CaII near-infrared (NIR) triplet, up to +5days relative to the SN B-band maximum light. We find that a high-velocity component of the CaII NIR triplet is needed to explain the spectrum in ~95% of SNe Ia observed before -5days, decreasing to ~80% at maximum. The average velocity of the CaII high-velocity component is ~8500km/s higher than the photospheric component. We confirm previous results that SNe Ia around maximum light with a larger contribution from the high-velocity component relative to the photospheric component in their CaII NIR feature have, on average, broader light curves and lower CaII NIR photospheric velocities. We find that these relations are driven by both a stronger high-velocity component and a weaker contribution from the photospheric CaII NIR component in broader light curve SNe Ia. We identify the presence of CII in very-early-time SN Ia spectra (before -10days), finding that >40% of SNe Ia observed at these phases show signs of unburnt material in their spectra, and that CII features are more likely to be found in SNe Ia having narrower light curves.