  We explore the ground-state properties of the two-band Hubbard model with
degenerate electronic bands, parametrized by nearest-neighbor hopping $t$,
intra- and inter-orbital on-site Coulomb repulsions $U$ and $U^\prime$, and
Hund coupling $J$, focusing on the case with $J>0$. Using Jastrow-Slater wave
functions, we consider both states with and without magnetic/orbital order.
Electron pairing can also be included in the wave function, in order to detect
the occurrence of superconductivity for generic electron densities $n$. When no
magnetic/orbital order is considered, the Mott transition is continuous for
$n=1$ (quarter filling); instead, at $n=2$ (half filling), it is first order
for small values of $J/U$, while it turns out to be continuous when the ratio
$J/U$ is increased. A significant triplet pairing is present in a broad region
around $n=2$. By contrast, singlet superconductivity (with $d$-wave symmetry)
is detected only for small values of the Hund coupling and very close to half
filling. When including magnetic and orbital order, the Mott insulator acquires
antiferromagnetic order for $n=2$; instead, for $n=1$ the insulator has
ferromagnetic and antiferro-orbital orders. In the latter case, a metallic
phase is present for small values of $U/t$ and the metal-insulator transition
becomes first order. In the region with $1<n<2$, we observe that ferromagnetism
(with no orbital order) is particularly robust for large values of the Coulomb
repulsion and that triplet superconductivity is strongly suppressed by the
presence of antiferromagnetism. The case with $J=0$, which has an enlarged
SU(4) symmetry due to the interplay between spin and orbital degrees of
freedom, is also analyzed.
