Hot Jupiters were many of the first exoplanets discovered in the 1990s, but in the decades since their discovery the mysteries surrounding their origins have remained. Here we present nine new hot Jupiters (TOI-1855 b, TOI-2107 b, TOI-2368 b, TOI-3321 b, TOI-3894 b, TOI-3919 b, TOI-4153 b, TOI-5232 b, and TOI-5301 b) discovered by NASA's TESS mission and confirmed using ground-based imaging and spectroscopy. These discoveries are the first in a series of papers named the Migration and Evolution of giant ExoPlanets survey and are part of an ongoing effort to build a complete sample of hot Jupiters orbiting FGK stars, with a limiting Gaia G-band magnitude of 12.5. This effort aims to use homogeneous detection and analysis techniques to generate a set of precisely measured stellar and planetary properties that is ripe for statistical analysis. The nine planets presented in this work occupy a range of masses (0.55M(J) < M-P < 3.88M(J)) and sizes (0.967R(J )< R-P < 1.438R(J)) and orbit stars that have an effective temperature in the range of 5360 K < T-eff < 6860 K with Gaia G-band magnitudes ranging from 11.1 to 12.7. Two of the planets in our sample have detectable orbital eccentricity: TOI-3919 b (e=0.259(-0.036)(+0.033)) and TOI-5301 b ( e=0.33(-0.10)(+0.11)). These eccentric planets join a growing sample of eccentric hot Jupiters that are consistent with high-eccentricity tidal migration, one of the three most prominent theories explaining hot Jupiter formation and evolution.