If your private is ASEL you can log PIC in any airplane single engine land. So a piper warrior, archer, C172, or C152 it doesn't matter. If you want to fly a complex single engine than you need an endorsement from an instructor. Ususally they will go up and fly a couple hours with you and give you the endorsement if they think you're competent. After that you can log PIC in any complex single engine or noncomplex single engine. So whethter it is an arrow or C172 it would all be PIC.