In the target-rich era of exoplanetary science, time on large-aperture telescopes will be at a premium, and more transmission spectroscopy studies will be conducted using distributed heterogeneous networks of small (< 3m) telescopes. To help the community prepare for the target-rich era, SPEARNET (the Spectroscopy and Photometry of Exoplanetary Atmospheres Research Network) are developing tools and techniques to facilitate making observations from such a network, and this thesis details work conducted as part of this. Ideally, observations made with a telescope network should be fitted simultaneously. In this thesis, I detail the development of TransitFit, an open-source Python 3 package designed to simultaneously fit transit light curves from multiple telescopes and filters. TransitFit has the ability to simultaneously detrend observations, and is unique among publicly-available codes in its ability to use host characteristics and filter profiles to inform the fitting of limb-darkening coefficients. I demonstrate the application of TransitFit to four planets, first analysing broadband photometric observations of WASP-127~b taken using the SPEARNET telescope network. I then provide updated ephemerides for WASP-91~b using TESS observations, and conduct a TTV analysis of WASP-126~b, finding no evidence of a companion planet in the system. Finally, I re-analyse spectroscopic HST observations of WASP-43~b, and find that detrending observations simultaneously with fitting transit parameters finds less evidence for water vapour in the transmission spectrum. As more spectroscopy studies are conducted, manually choosing priors for atmospheric parameter retrieval will become a time-consuming task, whilst using wide, uninformed priors will require longer run-times. I present a novel method of using machine learning classification to automatically generate informed priors, and show that this approach can offer a median speed-up of $15\%$ when applied to observations simulated for JWST and Twinkle.