A generalised theory has been used to carry out a comparative analysis of the use of various four-level and quasi-three-level media for the self-starting of degenerate four-wave mixing PCW generation directly in a laser medium placed in a loop resonator. It has been shown that quasi-three-level media can compete with four-level media at long upper laser level lifetimes and increased pump intensities. The most attractive solid-state laser media for four-wave PCW generation have been identified that have the highest deposited energy at a given pump intensity. In addition to neodymium-doped crystals, which are already widely used for four-wave PCW generation, promising materials are four-level chromium-doped media, e. g. alexandrite and Cr:LiCAF, and quasi-three-level media with the longest upper laser level lifetime, such as Yb:YAG and Tm, Ho:YAG, at high pump intensities.