If you're setting the game where they live, it's worth mentioning that the HP world has a school in Massachusetts called the Salem Witches' Institute. That might be your local school's "rival."
I've considered a HP RPG in the past, and my ideas were based on keeping things simple. Standard d20 is heavily geared toward combat, and an HP RPG should not be. Strength and Constitution make sense as two separate things for d20 games, but in HP it's easier to lump them together. Spells have to be at the center of everything, though the system should ideally be flexible enough to account for characters (like Hagrid) who focus more on skills and attributes than spells. Whimsical's Harry Potter GURPS sounds similar to the line of thinking I've had.
If I ever ran an OGL Harry Potter game, it would look like this:
- Four attributes (Toughness, Speed, Intelligence, Willpower) replace abilities and saving throws
- Simplified skills (Diplomacy and Bluff become Persuade, Hide and Move Silently become Sneak, Spot and Listen become Notice, etc.)
- A few extra skills (Care of Magical Creatures, Herbology, Muggle Studies, History of Magic) replace Knowledge skills
- Five basic "classes" of magic: Dueling Charms, Practical Charms, Potions, Transfiguration, and Dark Arts (which also includes Defense Against the Dark Arts)
- Magic is essentially skill-based and free-form; characters can cast a spell listed in the books or make up one of their own within one of the five classes
- Characters can spend one hit point to add 1d6 to any spell roll
- Characters can pick a few "favored spells" each level
- Levels, but no classes; point-based character creation
- Experience points are gained for achieving objectives, acting in-character, and creative spell use
- Feats and Flaws add additional flavor
- Combat revolves around disabling, disarming, and avoiding enemie
- Adventures are mysteries; characters have to overcome obstacles to find Hints, which take the place of treasure
*For example, a character with Practical Charms +7 confronted with a locked door might cast Alohomora. The GM could rule that a standard locked door is DC 15 to open, giving the character a better than even chance.
Of course, those are just some ideas that I never quite threw together. But I can't imagine it would take long to turn them into a real game. Combined with a few of the other systems here, you should have something up and running pretty quickly.