  To advance our understanding of the evolution of the interstellar medium
(ISM) of our Galaxy, numerical models of Milky Way (MW) type galaxies are
widely used. However, most models only vaguely resemble the MW (e.g. in total
mass), and often use imposed analytic potentials (which cannot evolve
dynamically). This poses a problem in asserting their applicability for the
interpretation of observations of our own Galaxy. The goal of this work is to
identify a numerical model that is not only a MW-type galaxy, but one that can
mimic some of the main observed structures of our Galaxy, using dynamically
evolving potentials, so that it can be used as a base model to study the ISM
cycle in a galaxy like our own. This paper introduces a suite of 15 MW-type
galaxy models developed using the {\sc arepo} numerical code, that are compared
to Galactic observations of $^{12}$CO and \ion{H}{I} emission via
longitude-velocity plots, from where we extract and compare the skeletons of
major galactic features and the terminal gas velocities. We found that our
best-fitting model to the overall structure, also reproduces some of the more
specific observed features of the MW, including a bar with a pattern speed of
$30.0 \pm 0.2$ km\,s$^{-1}$\,kpc$^{-1}$, a bar half-length of $3.2 \pm
0.8$\,kpc. Our model shows large streaming motions around spiral arms, and
strong radial motions well beyond the inner bar. This model highlights the
complex motions of a dynamic MW-type galaxy and has the potential to offer
valuable insight into how our Galaxy regulates the ISM and star formation.
