S. cerevisiae offers nice model to express and purify recombinant proteins. Generally the mostly used expression systems use GAL1 or CUP1 inducible promoters for this purpose. For GAL1, the expression vectors like pEGU, pEGT, pEGL were used commonly. In case of CUP1 expression vectors like pECU, pECT, pECL were used. These vectors also available with different tags like His, GST, myc, which makes the purification of recomb protein easy.
And as you told, other yeast species like Pichia pastoris is mostly used and recommended for recombinanat protein purification. pJAZ-αMF vector used mostly for this strain.