  In this contribution we briefly discuss an ongoing phenomenological programme
on quarkonium production in unpolarized and polarized proton-proton collisions
in a fixed target setup at LHCb, the LHCSpin project. Within a TMD approach, we
aim at considering in particular: the relative role of the NRQCD color-singlet
and color-octet production mechanisms, both for unpolarized and polarized
quarkonium production; the study of azimuthal and transverse single-spin
asymmetries as a phenomenological tool for learning about the almost unknown
gluon Sivers function; the role of initial- and final-state interactions for
spin asymmetries.
