We use early-time photometry and spectroscopy of 12 Type II plateau supernovae (SNe IIP) to derive their distances using the expanding photosphere method (EPM). We perform this study using two sets of Type II supernova (SN II) atmosphere models, three filter subsets ({BV}, {BVI}, and {VI}), and two methods for the host-galaxy extinction, which leads to 12 Hubble diagrams. We find that systematic differences in the atmosphere models lead to similar to 50% differences in the EPM distances and to a value of H(0) between 52 and 101 km s(-1) Mpc(-1). Using the {VI} filter subset we obtain the lowest dispersion in the Hubble diagram, sigma(mu) = 0.32 mag. We also apply the EPM analysis to the well observed SN IIP 1999em. With the {VI} filter subset we derive a distance ranging from 9.3 +/- 0.5 Mpc to 13.9 +/- 1.4 Mpc depending on the atmosphere model employed.