i read your long post, now you read mine
not sure if this was a mistake, but I did not see Evangelion on your list e.e
anyway, I recommend the Neon Genesis Evangelion series, The End of Evangelion film,
and The Rebuild of Evangelion film trilogy(tetralogy) .. (in that order)
people always recommend Gintama, and it has its good points, but it's a never-ending
referential comedy with hit-or-miss gags and cheesy Gintoki.. i however will recommend
Sket-Dance which is highly similar to Gintama (the author being a former
assistant to Gintama's author/manga), but idk, i loved the characters a lot more
and found it funnier and less repetitive.. though i would recommend the manga,
but the anime is just as great, it's just that the manga continues and has more
character moments and an emotional conclusion~
with the new sequel announced, you should watch Code Geass before you're
turned off from the series depending if the new anime sucks (which i'm pretty
sure it will), but regardless of that, Code Geass: Lelouch of the Rebellion and
R2 are still incredibly great
oh, and maybe you should watch Legend of the Galactic Heroes which is an
epic space opera.. though it's kinda old, it is 'epic' in every sense, but thinking
about it now as i'm writing this, it'll probably take up most of your break, and
probably not suitable for your "daughter" in the matter of it being mature and
its genius and intellectual story form requiring a high attention span...
and i don't see Hunter X Hunter (2011) on you list either, that's also a longer series,
but it's definitely one of the best shounen and though it's a little darker than
the more mainstream shounen, especially towards the end, its vibrant colors and
colorful cast feel like a shounen, but its a kinda subverting series of the genre
Kino's Journey is also great and short too (13 episodes)..
and this post is already too long, so let me lightning-round the rest, but even
though i didn't talk about them much doesn't mean they're less worth the watch
as those above~
Bakuman., Beck, Great Teacher Onizuka, Planetes, Maison Ikkoku, Spice and Wolf,
Hajime no Ippo, Fate/Zero, Chihayafuru, Blast of Tempest, Hanasaku Iroha,
Mawaru Penguindrum, NouCome, Working!!, Magical Shopping Arcade Abenobashi,
Nichijou and Kaiba
i know it's a lot, and i probably have a lot more i could recommend, but at least
read their synopsis, also.. i've underlined the ones that might not be suitable
for your "daughter" unless she's a teenager, but you could watch them on
your own regardless
not sure if your list was up to date, but that's what i based my recommendations on
(whether you've watched something or not)