If it's an aircraft your SEP rating permits you to fly (ie. not of a complex nature for which you have not received differences training), you are perfectly entitled to log P1. Discuss who is logging P1 with the instructor before the flight. You can log PU/T if you like, but why would you when you can log P1? The checkout is not a legal requirement, usually just a club/school protecting their aircraft. There would be nothing to stop you learning and qualifying entirely on say C152's, then going out and buying a non-complex PA28 and flying it away.
P1/S should only be logged for a successful flight test.