We provide results for the leading superconducting instabilities for a model pertaining to Sr2RuO4 obtained within spin-fluctuation mediated superconductivity in the very weak-coupling limit. The theory incorporates spin-orbit coupling (SOC) effects both in the band structure and in the pairing kernel in the form of associated magnetic anisotropies. The leading superconducting phase is found to be d(x2-y2) and a nodal s-wave state. However, the odd-parity helical solution can become leading either for small SOC and Hund's coupling J in the weak U-limit, or in the opposite limit with large SOC and J at larger values of the Hubbard-U. The odd-parity chiral solution is never found to be leading. Finally we discuss the form of the resulting superconducting spectral gaps in the different explored parameter regimes.