The Hubble Space Telescope (HST) has been our most prolific tool to study exoplanet atmospheres. As the age of JWST begins, there are a wealth of HST archival data that are useful to strengthen our inferences from JWST. Notably, HST/Space Telescope Imaging Spectrograph (STIS), with its 0.3–1 μm wavelength coverage, extends past JWST’s 0.6 μm wavelength cutoff and holds an abundance of potential information: alkali (Na, K) and molecular (TiO, VO) species opacities, aerosol information, and the presence of stellar contamination. However, time-series observations with HST suffer from significant instrumental systematics and can be highly dependent on choices made during the transit fitting process. This makes comparing transmission spectra of planets with different data reduction methodologies challenging, as it is difficult to discern whether an observed trend is caused by differences in data reduction or underlying physical processes. Here we present the Sculpting Hubble’s Exoplanet Legacy (SHEL) program, which aims to build a consistent data reduction and light-curve analysis methodology and associated database of transmission spectra from archival HST observations. In this paper, we present the SHEL analysis framework for HST/STIS and its low-resolution spectroscopy modes, G430L and G750L. We apply our methodology to four notable hot Jupiters, WASP-39 b, WASP-121 b, WASP-69 b, and WASP-17 b, and use these examples to discuss nuances behind analysis with HST/STIS. Our results for WASP-39 b, WASP-121 b, and WASP-17 b are consistent with past publications, but our analysis of WASP-69 b differs and shows evidence of either a strong scattering slope or stellar contamination. The data reduction pipeline and tutorials are available on Github and Zenodo.