  In numerical evolutions of binary black holes (BBH) it is desirable to easily
control the orbital eccentricity of the BBH, and the number of orbits completed
by the binary through merger. This paper presents fitting formulae that allow
to choose initial-data parameters for generic precessing BBH resulting in an
orbital eccentricity $\sim 10^{-4}$, and that allow to predict the number of
orbits to merger. We further demonstrate how these fits can be used to choose
initial-data parameters of desired non-zero eccentricity. For both usage
scenarios, no costly exploratory BBH evolutions are necessary, but both usage
scenarios retain the freedom to refine the fitted parameters further based on
the results of BBH evolutions. The presented fitting formulas are based on 729
BBH configurations which are iteratively reduced to eccentricity $\lesssim
10^{-4}$, covering mass-ratios between 1 and 8 and spin-magnitude up to 0.5.
101 of these configurations are evolved through the BBH inspiral phase.
