  Context: Being part of the brightest solar-like stars, and close solar
analogues, the 16 Cygni system is of great interest to the scientific community
and may provide insight into the past and future evolution of our Sun. It has
been observed thoroughly by the Kepler satellite, which provided us with data
of an unprecedented quality. Aims: This paper is the first of a series aiming
to extensively characterise the system. We test several choices of micro- and
macro-physics to highlight their effects on optimal stellar parameters and
provide realistic stellar parameter ranges. Methods: We used a recently
developed method, WhoSGlAd, that takes the utmost advantage of the whole
oscillation spectrum of solar-like stars by simultaneously adjusting the
acoustic glitches and the smoothly varying trend. For each choice of input
physics, we computed models which account, at best, for a set of seismic
indicators that are representative of the stellar structure and are as
uncorrelated as possible. The search for optimal models was carried out through
a Levenberg-Marquardt minimisation. First, we found individual optimal models
for both stars. We then selected the best candidates to fit both stars while
imposing a common age and composition. Results: We computed realistic ranges of
stellar parameters for individual stars. We also provide two models of the
system regarded as a whole. We were not able to build binary models with the
whole set of choices of input physics considered for individual stars as our
constraints seem too stringent. We may need to include additional parameters to
the optimal model search or invoke non-standard physical processes.
