  We investigate the feasibility of many candidate quantum Hall states for
two-component bosons in the lowest Landau level. We identify interactions for
which spin-singlet incompressible states occur at filling factors $\nu=2/3$,
4/5 and 4/3, and spin-partially-polarized states at filling factors 3/4 and
3/2, where "spin" serves as a generic label for the two components. We study
ground states, excitations, edge states and entanglement spectrum for systems
with up to 16 bosons, and construct explicit trial wave functions to clarify
the underlying physics. The composite fermion theory very accurately describes
the ground states as well as excitations at $\nu=2/3$, 4/5 and 3/4, although it
is less satisfactory for the $\nu=3/2$ state. For $\nu=4/3$ a "non-Abelian
spin-singlet" state has been proposed to occur for a 2-body contact
interaction; we find that it is more likely that the actual state here is a
spin-singlet state of reverse-flux-attached composite fermions at filling
$\nu^*=4$. We also consider incompressible states at integral filling factors
$\nu=1$ and 2. The incompressible state at $\nu=1$ is shown to be well
described by the parton-based Jain spin-singlet wave function, and the
incompressible state at $\nu=2$ as the spin-singlet state of
reverse-flux-attached composite fermions at $\nu^*=2$.
