  We use hydrodynamic cosmological zoom-in simulations from the FIRE project to
explore the morphologies and kinematics of fifteen Milky Way (MW)-mass
galaxies. Our sample ranges from compact, bulge-dominated systems with 90% of
their stellar mass within 2.5 kpc to well-ordered disks that reach $\gtrsim15$
kpc. The gas in our galaxies always forms a thin, rotation-supported disk at
$z=0$, with sizes primarily determined by the gas mass. For stars, we quantify
kinematics and morphology both via the fraction of stars on disk-like orbits
and with the radial extent of the stellar disk. In this mass range, stellar
morphology and kinematics are poorly correlated with the properties of the halo
available from dark matter-only simulations (halo merger history, spin, or
formation time). They more strongly correlate with the gaseous histories of the
galaxies: those that maintain a high gas mass in the disk after $z\sim1$
develop well-ordered stellar disks. The best predictor of morphology we
identify is the spin of the gas in the halo at the time the galaxy formed 1/2
of its stars (i.e. the gas that builds the galaxy). High-$z$ mergers, before a
hot halo emerges, produce some of the most massive bulges in the sample (from
compact disks in gas-rich mergers), while later-forming bulges typically
originate from internal processes, as satellites are stripped of gas before the
galaxies merge. Moreover, most stars in $z=0$ MW-mass galaxies (even $z=0$
bulge stars) form in a disk: $\gtrsim$60-90% of stars begin their lives
rotationally supported.
