Unless you go nuts with grinding, you very likely won't get this during your first playthrough. If you want to grind up before going into your Hard playthrough, the best way to grind exp and AP is in one of the combat arenas. You should do this after you beat the game, because that unlocks an exp and AP multiplier.
The best one I found was in the Shinra Combat Simulator in chapter 17 that unlocks once you've beaten the game. Choose chapter 17 from chapter select, and not too far (a few minutes) into the chapter you'll run across Chadley. In a room next door to him, there's a bench and vending machine, and in a room connected to that one is the combat simulator.
There are a lot of battles here, but you're specifically looking for ones that:
a) aren't too long or difficult
b) let you bring in your whole party
Fitting both these qualifications is the battle called "Three-Person Team vs. Team Ragbag". By the time you've beaten the game, the enemies shouldn't give you any real trouble, and the battles should take at most 4 minutes. (my first try I think took 3.5 minutes, by the end of grinding my record was 1:17) Even better, once you beat this battle once, you get an Exp Up materia! Equip that, and you'll be swimming in exp, probably getting a level for each character each one or two times you do the set of battles.
Make sure you have materia equipped that you want to level up! Especially if you're planning a Hard playthrough, you'll want levelled up Elemental, HP Up, MP Up, First Strike, Healing, Magnify, and Revival materia.