  We use cosmological hydrodynamic zoom-in simulations to study early structure
formation in two dark matter (DM) cosmologies, the standard CDM model, and a
thermal warm DM (WDM) model with a particle mass of $m_{\chi}c^{2}=3\
\mathrm{keV}$. We focus on DM haloes with virial masses $M\sim 10^{10}\
M_{\odot}$. We find that the first star formation activity is delayed by $\sim
200\ \mathrm{Myr}$ in the WDM model, with similar delays for metal enrichment
and the formation of the second generation of stars. However, the differences
between the two models in globally-averaged properties, such as star formation
rate density and mean metallicity, decrease towards lower redshifts ($z\lesssim
10$). Metal enrichment in the WDM cosmology is restricted to dense
environments, while low-density gas can also be significantly enriched in the
CDM case. The free-free contribution from early structure formation at
redshifts $z>6$ to the cosmic radio background (CRB) is $3_{-1.5}^{+13}\%$
($8_{-3.5}^{+33}\%$) of the total signal inferred from radio experiments such
as ARCADE 2, in the WDM (CDM) model. The direct detection of the
$\mathrm{H_{2}}$ emission from early structure formation ($z\gtrsim 7.2$),
originating from the low-mass haloes explored here, will be challenging even
with the next generation of far-infrared space telescopes, unless the signal is
magnified by at least a factor of 10 via gravitational lensing or shocks.
However, more massive haloes with $M\gtrsim 10^{12}\ M_{\odot}$ may be
observable for $z\gtrsim 10$, even without magnification, provided that our
extrapolation from the scale of our simulated haloes is valid.
