Have them play using a Sidekick class
Firstly, I agree with Carcer's answer that Fighter is the most straightforward class to play as. There is potentially some additional complexity with the archetype at 3rd level, but again, as Carcer say, picking Champion keeps things simple because it is such a simple archetype.
Taking this idea of simplicity further, the "Sidekick classes" presented in this Unearthed Arcana article includes simplified classes, including Warrior (which is much the same as a Champion Fighter), Expert (which is kind of like a Rogue but with a few Bard abilities and such mixed in), and Spellcaster (loosely based on a Wizard, but can be used with any spellcasting classes' spell list).
These classes are designed to be simple, much like the Champion, but the main advantage of them is that if your daughter does not want to play as a Fighter, these options cover a lot of other roles. Since none of them have archetypes, that doesn't open up more complexity like the standard classes do.
The Expert class does seem to fill more of an assistant role, so this one may make your child feel like their PC isn't as important as the PCs they're helping, so it may be better to simply pick Rogue, which comes with archetypes at 3rd level and all the other problems that come with picking from the standard classes.
Honestly, this answer is mostly about promoting the Spellcaster class. Magic is cool and fun! I can easily imagine a child wanting to play as a character who can cast spells, but spellcasting classes can be more complicated at the best of times (spell slots, choosing spells on level up, preparing spells if your that kind of caster, etc.), without including archetypes and extra features (such as Metamagic for Sorcerers, Eldritch Invocations for Warlocks, etc).
The Spellcaster class presents an option for playing a simpler spellcasting character that still lets you sling spells around, which is what a child will want to do, but without the extra features that the standard spellcasting classes also include.
Maybe mum can play one of these as well?
You said that mum will be there to help, but then she may find herself juggling two characters. Depending on how difficult that may be (I don't know how experienced she is, so I'm going to assume that it might caused extra difficult, because if it doesn't then my advice doesn't apply anyway so can be ignored), it might be useful for both your partner and your daughter to play as Sidekick classes so that it's easier on your partner to juggle the rules of both classes.
Indeed, if your daughter is going to be the central character of this adventure, then it might even be good for your partner to play as an Expert so that she can help your daughter's PC using the Helpful and Inspiring Help features of that class, thus making it more likely for your daughter's PC to do awesome things? But that depends on what character your partner wants to play...
All in all, these Sidekick classes could be useful (not so much Warrior, since a Champion Fighter would suit just as well) if your child does not want to play as a Warrior.