Recent detections of thermal inversions in the dayside atmospheres of some hot Jupiters are motivating new avenues to understand the interplay between their temperature structures and other atmospheric conditions. In particular, TiO has long been proposed to cause thermal inversions in hot Jupiters, depending on other factors such as stellar irradiation, C/O, and vertical mixing. TiO also has spectral features in the optical and near-infrared that have been detected. However, interpretations of TiO signatures rely on the accuracy of TiO opacity used in the models. The recently reported Toto TiO line list provides a new opportunity to investigate these dependencies, which is the goal of the present work. First, we investigate how the Toto line list affects observable transmission and emission spectra of hot Jupiters at low and high resolution. The improvement in the Toto line list compared to a previous line list results in observable differences in the model spectra, particularly in the optical at high resolution. Secondly, we explore the interplay between temperature structure, irradiation and composition with TiO as the primary source of optical opacity, using 1D self-consistent atmospheric models. Among other trends, we find that the propensity for thermal inversions due to TiO peaks at C/O$\sim$0.9, consistent with recent studies. Using these models, we further assess metrics to quantify thermal inversions due to TiO, compared to frequently-used Spitzer photometry, over a range in C/O, irradiation, metallicity, gravity and stellar type.