  Recent neutron scattering experiments addressing the magnetic state of the
two-leg ladder selenide compound BaFe$_2$Se$_3$ have unveiled a dominant spin
arrangement involving ferromagnetically ordered 2$\times$2 iron-superblocks,
that are antiferromagnetically coupled among them (the "block-AFM" state).
Using the electronic five-orbital Hubbard model, first principles techniques to
calculate the electronic hopping amplitudes between irons, and the real-space
Hartree-Fock approximation to handle the many-body effects, here it is shown
that the exotic block-AFM state is indeed stable at realistic electronic
densities close to $n \sim 6.0$. Another state (the "CX" state) with parallel
spins along the rungs and antiparallel along the legs of the ladders is close
in energy. This state becomes stable in other portions of the phase diagrams,
such as with hole doping, as also found experimentally via neutron scattering
applied to KFe$_2$Se$_3$. In addition, the present study unveils other
competing magnetic phases that could be experimentally stabilized varying
either $n$ chemically or the electronic bandwidth by pressure. Similar results
were obtained using two-orbital models, studied here via Lanczos and DMRG
techniques. A comparison of the results obtained with the realistic selenides
hoppings amplitudes for BaFe$_2$Se$_3$ against those found using the hopping
amplitudes for pnictides reveals several qualitative similarities, particularly
at intermediate and large Hubbard couplings.
