We report a systematic first-principles investigation of the influence of different magnetic insulators on the magnetic proximity effect induced in graphene. Four different magnetic insulators are considered: two ferromagnetic europium chalcogenides namely EuO and EuS and two ferrimagnetic insulators yttrium iron garnet (YIG) and cobalt ferrite (CFO). The obtained exchange-splitting in graphene varies from tens to hundreds of meV depending on substrates. We find an electron doping to graphene induced by YIG and europium chalcogenides substrates, that shift the Fermi level above the Dirac cone up to 0.78 eV and 1.3 eV respectively, whereas hole doping shifts the Fermi level down below the Dirac cone about 0.5 eV in graphene/CFO. Furthermore, we study the variation of the extracted exchange and tight-binding parameters as a function of the EuO and EuS thicknesses. We show that those parameters are robust to thickness variation such that a single monolayer of magnetic insulator can induce a strong magnetic proximity effect on graphene. Those findings pave the way towards possible engineering of graphene spin-gating by proximity effect especially in view of recent experimental advancements.