  We present Milky Way-est, a suite of 20 cosmological cold-dark-matter-only
zoom-in simulations of Milky Way (MW)-like host halos. Milky Way-est hosts are
selected such that they (i) are consistent with the MW's measured halo mass and
concentration, (ii) accrete a Large Magellanic Cloud (LMC)-like ($\approx
10^{11}~M_{\odot}$) subhalo within the last $2~\mathrm{Gyr}$ on a realistic
orbit, placing them near $50~\mathrm{kpc}$ from the host center at $z\approx
0$, and (iii) undergo a $>$1:5 sub-to-host halo mass ratio merger with a
Gaia-Sausage-Enceladus (GSE)-like system at early times ($0.67<z<3$). Hosts
satisfying these LMC and GSE constraints constitute $< 1\%$ of all halos in the
MW's mass range, and their total masses grow rapidly at late times due to LMC
analog accretion. Compared to hosts of a similar final halo mass that are not
selected to include LMC and GSE analogs, Milky Way-est hosts contain $22\%$
more subhalos with present-day virial masses above $10^8~M_{\odot}$ throughout
the virial radius, on average. This enhancement reaches $\approx 80\%$ in the
inner $100~\mathrm{kpc}$ and is largely, if not entirely, due to LMC-associated
subhalos. These systems also induce spatial anisotropy in Milky Way-est subhalo
populations, with $\approx 60\%$ of the total subhalo population within
$100~\mathrm{kpc}$ found in the current direction of the LMC. Meanwhile, we
find that GSE-associated subhalos do not significantly contribute to
present-day Milky Way-est subhalo populations. These results provide context
for our Galaxy's dark matter structure and subhalo population and will help
interpret a range of measurements that are currently only possible in the MW.
