I think it's better to know before-hand that the dungeons in P3 are basically all the same. I try to reach the top floor available in one trip to the tartarus and then play the regular school days as if it was a VN. Clearing quests and rescuing people that get lost in the tartarus gives me the extra grinding I need.
This is definitely the best version of P3 available. You can watch the missing chapter (The Truth) in youtube anyways.
Good point. It was the first Persona game I played and I didn't know much about it going in.