Definitely not a conifer, unless I'm getting mixed up...aren't they the ones that are quite ugly and just grow straight up for miles? Not even nice to look at imho.
In defence of horse chesnut trees, ours is at the end of our front garden and is stunning. When you drive into our road, it's the first thing you see, and it always warms my heart.
Agree that they grow to be absolutely huge, and agree about neighbours - our neighbours opposite said "I hope you'll be cutting that bloody tree down!" when we moved in.
It's not true, though, that nothing can grow under it.
I think they are really majestic, the motion when there is even the slightest breeze is beautiful, they are unique - have never seen other types of tree move in the same way.
Having said all that, they shed sticky buds all over the place once a year, that stick to your shoes and end up all over the house (this could be avoided if you have the sort of house where people take off their shoes, and DCs don't play out in their socks!)
If we ever moved, I would miss the tree as much as the house, but I'm not sure I'd plant one if I moved, iyswim, unless I had an absolutely huge garden.
Your description of your DD reminds me of me when I was little. When I was a child, we had a cooking apple tree in our garden which was the best tree ever for climbing and sitting in. My parents cut it down to grow bedding plants under it
..anyway, I'd consider that type of tree for a girl who loves trees!