  We consider `minimal' Z' models, whose phenomenology is controlled by only
three parameters beyond the Standard Model ones: the Z' mass and two effective
coupling constants. They encompass many popular models motivated by grand
unification, as well as many arising in other theoretical contexts. This
parameterization takes also into account both mass and kinetic mixing effects,
which we show to be sizable in some cases. After discussing the interplay
between the bounds from electroweak precision tests and recent direct searches
at the Tevatron, we extend our analysis to estimate the early LHC discovery
potential. We consider a center-of-mass energy from 7 towards 10 TeV and an
integrated luminosity from 50 to several hundred pb^-1, taking all existing
bounds into account. We find that the LHC will start exploring virgin land in
parameter space for M_Z' around 700 GeV, with lower masses still excluded by
the Tevatron and higher masses still excluded by electroweak precision tests.
Increasing the energy up to 10 TeV, the LHC will start probing a wider range of
Z' masses and couplings, although several hundred pb^-1 will be needed to
explore the regions of couplings favored by grand unification and to overcome
the Tevatron bounds in the mass region around 250 GeV.
