To realize effective van der Waals (vdW) transistors, vdW dielectrics are needed in addition to vdW channel materials. We study the dielectric properties of 32 exfoliable vdW materials using first principles methods. We calculate the static and optical dielectric constants and discover a large out-of-plane permittivity in GeClF, PbClF, LaOBr, and LaOCl, while the in-plane permittivity is high in BiOCl, PbClF, and TlF. To assess their potential as gate dielectrics, we calculate the band gap and electron affinity, and estimate the leakage current through the candidate dielectrics. We discover six monolayer dielectrics that promise to outperform bulk HfO2: HoOI, LaOBr, LaOCl, LaOI, SrI2, and YOBr with low leakage current and low equivalent oxide thickness. Of these, LaOBr and LaOCl are the most promising and our findings motivate the growth and exfoliation of rare-earth oxyhalides for their use as vdW dielectrics.