  The first stars hold intrinsic interest for their uniqueness and for their
potential importance to galaxy formation, chemical enrichment, and feedback on
the intergalactic medium (IGM). The metal-free composition of the first stars
restricts the stellar energy source to proton-proton burning rather than the
more efficient CNO cycle. Consequently they are hotter, smaller, and have
harder spectra than their present-day counterparts of finite metallicity. We
present new results from a continuing study of metal-free stars from a
cosmological point of view. We have calculated evolving spectra of Pop III
clusters, derived from a grid of zero-metallicity stellar evolutionary tracks.
We find that H-ionizing photon production from metal-free stellar clusters
takes twice as long as that of Pop II to decline to 1/10 its peak value. In
addition, metal-free stars produce substantially more photons than Pop II in
the HeII ($E > 4$ Ryd) continuum. We suggest that large Ly$\alpha$ equivalent
widths ($W_{\rm Ly\alpha} > 400$ Angstroms) may provide a means of detecting
metal-free stellar populations at high redshift, and that HeII recombination
lines ($\lambda$1640, $\lambda$4686) may confirm identifications of Population
III. While Pop III clusters are intrinsically bluer than their Pop II
counterparts, nebular continuum emission makes up this difference and may
confuse attempts to discern Pop III stars with broadband colors. In a companion
paper, we explore the consequences of evolving spectra of Pop III for the
reionization of the IGM in both H and He. (ABRIDGED)
