  We are conducting a large observing program with the Spitzer Space Telescope
to determine the mid-to-far infrared spectral energy distributions of a
well-defined sample of 87 nearby, 12 micron-selected Seyfert galaxies. In this
paper we present the results of IRS low-resolution spectroscopy of a
statistically representative subsample of 51 of the galaxies (59%), with an
analysis of the continuum shapes and a comparison of the Seyfert types. We find
that the spectra clearly divide into groups based on their continuum shapes and
spectral features. Some spectral features are clearly related to a starburst
contribution to the IR spectrum, while the mechanisms producing observed
power-law continuum shapes, attributed to an AGN component, may be dust or
non-thermal emission. The infrared spectral types appear to be related to the
Seyfert types. Principal component analysis results suggest that the relative
contribution of starburst emission may be the dominant cause of variance in the
observed spectra. We find that Sy 1's have higher ratios of IR/radio emission
than Sy 2's, as predicted by the unified model if the torus is optically thick
in the mid-IR. However, smooth-density torus models predict a much larger
difference between type 1's and 2's than observed in our sample. Our
observations may be consistent with clumpy torus models containing a steep
radial distribution of optically thick dense clumps. (Abridged)
