With over 4,000 exoplanet discoveries to date, we have caught a glimpse of the broad diversity of planets that span a range of masses, compositions, and orbital configurations. The next chapter in exoplanet exploration will focus on probing the atmospheres of these worlds, and we are now poised to begin large-scale atmospheric studies of exoplanets with current instruments on the Hubble Space Telescope (HST) via transmission spectroscopy. The HST Panchromatic Comparative Exoplanetology Treasury (PanCET) program has assembled the first statistically significant sample of exoplanet atmospheric observations in the ultraviolet, optical, and infrared. Here, I present precise optical to infrared (~0.3-5.0 microns) transmission spectra taken as part of PanCET using combined HST and Spitzer transit observations for the hot Jupiters WASP-52b, HAT-P-32Ab, and WASP-62b. I compare the transmission spectra of these planets to a grid of 1D radiative-convective forward models and retrieve the planetary atmospheric properties. Since WASP-52b orbits an active star, I expand upon current methods for disentangling stellar and planetary signals, and measure a precise planetary spectrum consistent with clouds as well as evidence of weak sodium absorption. For HAT-P-32Ab, I show that previous a priori predictions for the presence of clouds in gaseous planets based on trends in surface gravity and equilibrium temperature become muddled as we expand the number of planets with atmospheric observations. Finally, I find a cloud-free, haze-free atmosphere and tentative evidence of silicate absorption for WASP-62b, the only transiting giant planet in the James Webb Space Telescope (JWST) Continuous Viewing Zone. Expanding efforts for comparative exoplanetology, these optical to infrared observations constrain the atmospheric chemical composition of the most favorable targets well-suited for follow-up with JWST.