The discovery of the first fast radio burst (FRB) in 2007 opened a new frontier in the field of time-domain astrophysics. FRBs are bright, millisecond pulses of radio emission whose dispersed signals indicate an extragalactic origin. However, their physical origins remain a mystery, in large part due to the small number of precisely localized events and hence the lack of astrophysical context through host associations. Moreover, with only a small number of redshift measurements, their extraordinary utility as cosmological probes has not yet been realized. The era of FRB science is now poised to enter a new regime thanks to late-2023 upgrades to the CHIME/FRB experiment. Specifically, CHIME/FRB will single-handedly increase the rate of <1" FRB localizations by two orders of magnitude. Here we propose a Gemini Large and Long Program (LLP) to obtain GMOS spectroscopy of 200 FRB host galaxies discovered and localized by CHIME/FRB, 8 times larger than all known hosts collected over the past 10 years. We will (i) build the first homogeneous sample with enough statistical power to address the origins of repeating and non-repeating FRBs and model their stellar populations, (ii) extend the distribution to z>1 to place constraints on cosmological parameters, the circumgalactic medium and the cosmic web, and (iii) unveil sub-populations that diversify the host population. We expect this program to provide a gold standard catalog in the fields of transients and cosmology that will be made available for community use.