Dynamical response theory is employed to investigate the effects of various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths and density parameters . In the regime of a thin quantum wire, electrons are treated as a one-dimensional gas under different confinement models via effective electron-electron interaction potentials. Using the first-order random phase approximation (FRPA) including self-energy and exchange contribution, which provides the ground-state structure beyond the random phase approximation, we numerically compute the structure factor, pair-correlation function, correlation energy, and ground-state energy for various values of and . Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire in the high-density limit, we find that the correlation energy for transverse confinement models (harmonic), (cylindrical), and (harmonic-delta) approaches a.u., which agrees with the exact results in this limit [P.-F. Loos, J. Chem. Phys. 138, 064108 (2013); V. Ashokan, et al., Phys. Rev. B 101, 075130 (2020)]. This clearly illustrates that for at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance to yield the same correlation energy. In contrast, other confinement potentials, (infinite square well), (infinite square-infinite triangular well), and (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to a.u. for these potentials. The percentage difference in correlation energy between the confinement models and is within about in the high-density limit. The ground-state properties obtained from the FRPA are compared with the available quantum Monte Carlo results in the high-density regime. We observe that the peak height in the static structure factor at depends significantly on the confinement model. These prominent peaks at are fitted with a function based on our finite wire-width theory, guided by insights from bosonization, demonstrating good agreement with our FRPA theory.