Flying from the RHS is a little different. If the club/owner/school doesn't insist on a RHS checkout (like mine does) it's a good idea to do a few touch and gos from the RHS, with an experienced PPL (or instructor) in the LHS.
The other can of worms is indeed payment. The P1/PPL has to pay at least an equal share of the direct costs of the flight, or it starts to become "aerial work". In the case of the student owning the airplane, but legally just being a passenger along for the ride, I guess the student can invite two other pax, and pay the share for those pax as well. Nothing illegal in that. So then the P1/PPL only pays 1/4 of the direct costs.