Movie wise, anything by - Makoto Shinkai some are only 46-60 odd minutes long.
so
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5 Centimeters Per Second
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Voices of a Distant Star
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The Garden of Words
being very very good 3 to start with
personally my one of my favourite anime movies was
Sky Blue, its old but still good and one of the movies i'v seen many times.
Origin: Spirits of the Past also a good movie.
As for TV series -
for school mystery/fantasy/ghosts one of my favourites is still
tasogare otomex amnesia aka dusk maiden of amnesia.
For pure amazement and entertainment value i love the
bakemongatari series, full of witty word play very fun fight scenes and amazing design work, but it can be very confusing and hard to follow for a lot of people. Mostly consists of talking for 40 mins an episode with little action in between, but still if you stick with it you will love it. There's a lot of sequels to it
http://en.wikipedia.org/wiki/Monogatari_%28series%29
Can never go wrong with
Angel beats but bring tissues for the ending, the series will make you laugh uncontrollably then cry uncontrollably.
Anohana is the same.
Durarara!! is the one you want for day to day viewing its second season has just started airing too! For the plot and general story line you need to pay very close attention since it time skips A LOT, it shows the daily events happening between 20 odd cast members and how they all interact and progress their lives and certain events. Arguably its main heroine is also a Dullahan otherwise more commonly known as an irish headless horseman.
Baccano! is also kinda related and a classic, has high praise from everyone who has seen it. Its set in the same world as dura but in 1940s ish but does have some guest appearances of cast members show up in dura. But you need to watch baccano first to be able to spot them, btw its about alchemists and gaining immortality and is character heavy and likes to time skip to different peoples perspectives like dura.
As a last one i'll throw in
psycho pass for a crime sci fi series, its definitely one of the better shows to watch.
Hope you enjoy if you decide to go with any of these ^^