Fate Accelerated

As for fit to purpose, i'm not sure that Fate Accelerated is the one I will be using for the kids. It is certainly aimed, in some ways, at a younger set, with lots of recommendations that you play as your favourite characters - such as a young wizard at a school for wizardry, along with other less-than-subtle-but-not-completely-spelled-out pop culture references. That's why I thought it might be a good choice.
Generic roleplaying systems aren't a new thing; there have been many attempts to create a roleplaying system that allows you to play any setting, any type of game with one set of rules. Generally they haven't been hugely successful, though some have been successful enough to set up in niches of their own. (GURPS springs to mind here, whose simulationist approach and high standards of research have resulted in some amazing material that even people who don't like GURPS itself buy as reference material.)
FATE's approach to this, particularly fate accelerated, is to slim down the rules entirely to a rather intriguing idea of "aspects" and "approaches". Rather than a character sheet full of skills and attributes seeking to simulate the world, a character is made up of statements and properties such as "The fastest draw in the west" and "Captain of the starship excelsior", which can be brought into play to give a bonus to any roll where they might be argued to apply. FATE is a narrative game taken far over to the narrative side of the rpg fence, where the storygamers live, with all the shared worldbuilding, consensus gameplay and improvised stories that are part of that 'style' of roleplaying. To be honest, it is an intriguing system that I will like to put to the test some day.
What it lacks, however, is structure. Whilst some games (GURPS springs to mind again, as well as Pathfinder and D&D 3.5) built up so much structure, rules and exceptions that the game could easily topple under the weight of them, with GM's and player's alike lost trying to remember the rules to the game they were playing, Fate accelerated throws most of that out of the window in storygame fashion, giving a simple couple of mechanical rules and challenging the players and particularly the GMs to handle the heavy lifting and exceptions in narrative, with creative use of aspects.
It sounds fun, however for a first game with my little ones, I'm looking for something with a bit more structure to it.
Still, definitely worth a good look if you want something mechanically simple but capable of serving as a base for complex stories, or if you want something that you can use to run a game on very short notice, with little preparation.