RPG

I tend to have a few standard recommendations for requests like this, but some don't necessarily fit as well with the wizard-centered setting you're suggesting.

The ones I think might fit best include:

Little Wizards - (also in paperback ) This is almost exactly what you are asking for: Characters are young magicians in a relatively mundane world. Might be stretched slightly to run Harry Potter or Kiki's Delivery Service type of setting. The art is colorful and evocative. In the game system failure can cause setbacks and require new solutions to problems, but total defeat or death is not specifically represented.

Risus – A very simple, very general system, not attached to one particular genre or setting. Some adventures here. You could easily use it to run many types of games. The author also has a lot of advice on running a game here.

Folklore: A Rules-Light Roleplaying Game - Another simple, universal game that can probably do any genre. At only four pages (pamphlet sized) this is one of the shortest, simplest. But pretty much no existing material for it.

Hero Kids - Cheap, relatively simple fantasy roleplaying game. Mostly for tactical play. Should work pretty well with kids who are into miniatures or board games. Many character choices and adventures. Probably not closer to Harry Potter type themes, but it does have several types of magicians.

Also, only mentioning the following in case you need something really closer to regular D&D rules, but simpler than standard 5th Edition D&D:

Swords & Wizardry - This is a clone of an earlier version of D&D, but with things cleaned up and made more elegant and clear. There are different editions of this game, tailored to the amount of additional information and detail folks want.

Old-School Essentials - This is another game designed in a similar way, but based on a different earlier edition of D&D.