  We identify ground states of one-dimensional fermionic systems subject to
competing repulsive interactions of finite range, and provide phenomenological
and fundamental signatures of these phases and their transitions. Commensurable
particle densities admit multiple competing charge-ordered insulating states
with various periodicities and internal structure. Our reference point are
systems with interaction range $p=2$, where phase transitions between these
charge-ordered configurations are known to be mediated by liquid and
bond-ordered phases. For increased interaction range $p=4$, we find that the
phase transitions can also appear to be abrupt, as well as being mediated by
re-emergent ordered phases that cross over into liquid behavior. These
considerations are underpinned by a classification of the competing
charge-ordered states in the atomic limit for varying interaction range at the
principal commensurable particle densities. We also consider the effects of
disorder, leading to fragmentization of the ordered phases and localization of
the liquid phases.
