Agree. Start with a good read of the POH. Start with a quick read from cover to cover, and then:
Do a few mock W&B calculations, and a few TO/LD distance calculations in various configurations and circumstances. Compare the results to similar calculations for an aircraft type you know (C172 in your case).
Take the authorized operators (normal and emergency) checklist, compare it to the POH checklist to see if there are any differences, and find an explanation for these differences.
Look up the various reference speeds. Vr, Vx, Vy, cruise settings (with leaning instructions), Vref, Vs, Va, Vno, Vne.
Take a good look at the various systems. Fuel, electrics, ... Especially the PA28 fuel system is more involved than the C172s system: You've got to switch tanks every now and then; there is no "both" setting, and as a low-wing it's got a fuel pump which needs to be on for certain phases of flight. On the plus side, refueling doesn't need a stepladder.
Other things you will notice:
- Only one door, but it's secured with two independent latches. If flying with passengers, entry and (emergency) egress need to be thought out beforehand.
- Manual flaps instead of electric.
- The fuel selector is in a location where you will not readily see it, and it's all to easy to forget about it.
- The carb heat knob is relatively flimsy.
- Throttle and mixture are levers instead of plungers.
- I find the landing gear more forgiving than the C172, due to the oleos which provide some damping of a hard landing. Where a C172 will throw you back into the air, and then bounce you on the nosewheel.
- High wing vs. low wing obviously leads to a different view out the window. No need to lift a wing before turning, but the visibility downwards is less.