The many-body ground state wave function of a fractional Chern insulator (FCI) can be constructed by mapping a fractional quantum Hall state to a FCI state through a substitution of the Bloch state of the flat Chern band for the magnetic Bloch state of the Landau level. There is a gauge freedom in choosing the single particle Bloch basis of the flat Chern band. Instead of considering only one form of interaction in FCI when choosing the gauge as done in previous works, we determine the optimal gauges for FCIs with different forms of interaction, including a short-range interaction, the Coulomb interaction, and an interpolation between them, by applying the variational principle proposed by Zhang et al. [Phys. Rev. B 93, 165129 (2016)]. We find that the optimal gauge strongly depends on the form of interaction. It contradicts with the common belief that the wave function of FCI is not sensitive to the interaction. In comparing the optimal gauge with the previous gauges proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] and Wu et al. [Phys. Rev. B 86, 085129 (2012)], we find Wu et al.'s gauge is close to the optimal one when the interaction is a certain mixture of the Coulomb interaction and the short-range interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases.