A method for processing feedstock is described, characterized in that incoming feedstock is processed to selectively recover biogenic carbon material from the incoming feedstock. In some embodiments the incoming feedstock is comprised of mixed solid waste, such as municipal solid waste (MSW). In other embodiments the incoming feedstock is comprised of woody biomass. In some instances, the incoming feedstock is processed to selectively recover biogenic carbon material from the incoming feedstock to produce a processed feedstock having biogenic carbon content of 50% and greater suitable for conversion into biogenic carbon Fischer Tropsch liquids. The high biogenic carbon Fischer Tropsch liquids may be upgraded to biogenic carbon liquid fuels. Alternatively, the incoming feedstock is processed to selectively recover plastic material from the incoming feedstock to produce a processed feedstock having biogenic carbon content of 50% or less.