  We present the influences of electronic and magnetic correlations and doping
evolution on the groundstate properties of recently discovered superconductor
Ba$_{2}$CuO$_{4-\delta}$ by utilizing the Kotliar-Ruckenstein slave boson
method. Starting with an effective two-orbital Hubbard model (Scalapino {\it et
al.} Phys. Rev. {\bf B 99}, 224515 (2019)), we demonstrate that with increasing
doping concentration, the paramagnetic (PM) system evolves from two-band
character to single-band ones around the electron filling n=2.5, with the band
nature of the $d_{3z^{2}-r^{2}}$ and $d_{x^{2}-y^{2}}$ orbitals to the
$d_{x^{2}-y^{2}}$ orbital, slightly affected when the electronic correlation U
varies from 2 to 4 eV. Considering the magnetic correlations, the system
displays one antiferromagnetically metallic (AFM) phase in $2<n<2.16$ and a PM
phase in $n>2.16$ at U=2 eV, or two AFM phases in $2<n<2.57$ and $2.76<n<3$,
and a PM phase in $2.57<n<2.76$ respectively, at U=4 eV. Our results show that
near realistic superconducting state around n=2.6 the intermediate correlated
Ba$_{2}$CuO$_{3,2}$ should be single band character, and the s-wave
superconducting
  pairing strength becomes significant when U$>$2 eV, and crosses over to
d-wave when U$>$2.2 eV.
