As a follow-up of the high-pressure synthesis and the structural determination of two new ${\text{BaIrO}}_{3}$ polytypes, we report in this paper a systematic study of the physical properties of all polytypes available to us through measurements of magnetic, electronic transport, thermodynamic, and low-temperature structural as well as pressure effects. With increasing fraction of the corner- to face-sharing octahedra in the sequence $9R$ $(hhChhChhC)\ensuremath{\rightarrow}5H(hChCC)\ensuremath{\rightarrow}6H(hCChCC)$, the ground states of ${\text{BaIrO}}_{3}$ evolve from a ferromagnetic insulator with ${T}_{\text{c}}\ensuremath{\approx}180\text{ }\text{K}$ in the $9R$ phase to a ferromagnetic metal with ${T}_{\text{c}}\ensuremath{\approx}50\text{ }\text{K}$ in the $5H$ phase, and finally to an exchange-enhanced paramagnetic metal near a quantum critical point (QCP) in the $6H$ phase. The experimental results for the $9R$ phase confirm that the ferromagnetic transition is accompanied by a lattice instability, presumably associated with the formation of a charge density wave. The evidence includes a sudden increase in resistivity and thermoelectric power, an anomaly in the thermal conductivity, an unusual expansion of the $c$ axis, and an extraordinarily large pressure coefficient of ${T}_{\text{c}}$. In contrast, the ferromagnetic transition in the $5H$ ${\text{BaIrO}}_{3}$ only gives rise to weak anomalies in the resistivity and specific heat near ${T}_{\text{c}}$, similar to ${\text{SrRuO}}_{3}$; the $5H$ phase is the first weak ferromagnetic metal among the known oxide iridates. The $6H$ phase remains a paramagnetic metal to the lowest temperature. However, a strongly enhanced thermoelectric power and a non-Fermi-liquid behavior from the resistivity measurement at low temperature show that quantum critical fluctuations play a role in this exchange-enhanced paramagnetic phase. A positive thermoelectric power confirms the charge carriers are holelike for all polytypes, which is consistent with the electronic configuration of Ir(IV) $(5{d}^{5})$ in the low-spin state. The low-temperature specific-heat coefficients and Sommerfeld-Wilson ratios are in agreement with the evolution of the ground states across a ferromagnetic to paramagnetic QCP.