For example, the pPGKpuro from Addgene has a selectable marker, puromycin and a bacterial resistance, Ampicillin. According to my understanding, this plasmid confers resistance to both ampicillin and puromycin. Does that mean I can use either puromycin or ampicillin for screening?
Thanks.
Looking at the map of pPGKpuro from Addgene, it looks like you can only use ampicillin for selection in E. coli. The puromycin resistance gene is driven by a mammalian promoter, so unless there's a different bacterial promoter upstream of it that's unlabeled on the map, E. coli RNA polymerase isn't going to transcribe it. Puromycin is probably for selection in mammalian cell culture.
Usually when Addgene says "bacterial resistance" it means "selection for the plasmid in E. coli for cloning/plasmid maintenance" and "selectable marker" means it's an active marker when transferred to the organism of interest.