I am in a position I suspect many would be envious of. I've never seen any of these films. My first experience waits ahead!
Where should I begin? I have kids in the 10-15 year old bracket if people think they'd make a good family experience.
The order as presented in letterboxd is pretty spot on. The first 8 are the most accessible to audiences. After that it is more for a deep dive and/or completionists. I've seen the top 11, I should probably watch them all again sometime.
I tend to agree with ProZD's tier list[1] where "Kiki's Delivery Service", "Porco Rosso", and "Totoro" are at S rank. Those might also be a good introduction since they're pretty "normal".
Warning: I thought the first 10 minutes of Up were the saddest thing I'd ever watch, but then I watched Grave of the Fireflies.
Spirited Away is my absolute favorite one and I think great for children too. Mononoke, Porco Rosso, and Nausicaa are maybe more serious/mature but still incredible. Other valid options especially for children: Totoro, Ponyo, Howl's Moving Castle.
In any case you're in for an adventure!
What an fantastic problem to have! A few Ghibli films are a tad too odd or serious in tone for a movie night, but I can heartily recommend Ponyo, M.N. Totoro, and Spirited Away, the first being probably the most light-hearted and simple fun.
I’d start win this order:
Spirited away
Howls moving castle
Princess Mononoke
Castle in the sky
NausicaaLike others I would recommend starting with spirited away, should be suitable, and enjoyable for kids in 10-15 bracket.
Start with "My Neighbor Totoro"
Spirited Away.
I can't recommend a specific order but...
If looking for "adventure" go with Laputa, Cagliostro, maybe Porco Rosso.
If looking for something "warm" go with Totoro, Kiki, Ponyo.
If looking for something more "fantastical" (probably also more complex) try Howl's, Spirited Away, Nausicaä, Mononoke.
If you are willing to consider a TV show, then Sherlock Hound is really fun and delightful in every possible way. The complete series is IIRC 26 episodes.
Also, there are some non-Miyazaki but still Ghibli films which you may want to consider too. Personally, I absolutely love Mimi wo Sumaseba and I can hear the sea, but these may well be a bit uninteresting for a 10 year old; better for a teen probably over 15 I'd guess. Pompoko is clearly recommended for your age bracket though, and it's fun too.
Finally, there's the question of Grave of the Fireflies. I think 15 is probably fine, 10... maybe. But in any case, be warned that it's a very sad story and I have very rarely met someone who could watch it without crying profusely.