The last decade of observational and theoretical developments in stellar and binary evolution provides an opportunity to incorporate major improvements to the predictions from population synthesis models. We compute the Galactic merger rates for NS-NS, BH-NS, and BH-BH mergers with the StarTrack code. The most important revisions include updated wind mass-loss rates (allowing for stellar-mass black holes up to 80 M ☉), a realistic treatment of the common envelope phase (a process that can affect merger rates by 2-3 orders of magnitude), and a qualitatively new neutron star/black hole mass distribution (consistent with the observed "mass gap"). Our findings include the following. (1) The binding energy of the envelope plays a pivotal role in determining whether a binary merges within a Hubble time. (2) Our description of natal kicks from supernovae plays an important role, especially for the formation of BH-BH systems. (3) The masses of BH-BH systems can be substantially increased in the case of low metallicities or weak winds. (4) Certain combinations of parameters underpredict the Galactic NS-NS merger rate and can be ruled out. (5) Models incorporating delayed supernovae do not agree with the observed NS/BH "mass gap," in accordance with our previous work. This is the first in a series of three papers. The second paper will study the merger rates of double compact objects as a function of redshift, star formation rate, and metallicity. In the third paper, we will present the detection rates for gravitational-wave observatories, using up-to-date signal waveforms and sensitivity curves.
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