We report initial performance results emerging from 600 hours of observations with the Automated Planet Finder (APF) telescope and Levy Spectrometer located at UCO/Lick Observatory. We have obtained multiple spectra of 80 G, K and M-type stars, which comprise 4,954 individual Doppler radial velocity (RV) measurements with a median internal uncertainty of 1.35 ms$^{-1}$. We find a strong, expected correlation between the number of photons accumulated in the 5000-6200$AA$ iodine region of the spectrum, and the resulting internal uncertainty estimates. Additionally, we find an offset between the population of G and K stars and the M stars within the data set when comparing these parameters. As a consequence of their increased spectral line densities, M-type stars permit the same level of internal uncertainty with 2x fewer photons than G-type and K-type stars. When observing M stars, we show that the APF/Levy has essentially the same speed-on-sky as Keck/HIRES for precision RVs. In the interest of using the APF for long-duration RV surveys, we have designed and implemented a dynamic scheduling algorithm. We discuss the operation of the scheduler, which monitors ambient conditions and combines on-sky information with a database of survey targets to make intelligent, real-time targeting decisions.