We give an extensive description of the renormalisation of the Higgs sector of the minimal supersymmetric model in SloopS. SloopS is an automatised code for the computation of one-loop processes in the MSSM. In this paper, the first in a series, we study in detail the non gauge invariance of some definitions of tan(beta). We rely on a general non-linear gauge fixing constraint to make the gauge parameter dependence of different schemes for tan(beta) at one-loop explicit. In so doing, we update, within these general gauges, an important Ward-Slavnov-Taylor identity on the mixing between the pseudo-scalar Higgs, A^0, and the Z^0. We then compare the tan(beta) scheme dependence of a few observables. We find that the best tan(beta) scheme is the one based on the decay A^0 -> tau^+ tau^- because of its gauge invariance, being unambiguously defined from a physical observable, and because it is numerically stable. The oft used DRbar scheme performs almost as well on the last count, but is usually defined from non-gauge invariant quantities in the Higgs sector. The use of the heavier scalar Higgs mass in lieu of tan(beta) though related to a physical parameter induces too large radiative corrections in many instances and is therefore not recommended.
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