What is the best anime of all time?

Your asking two different questions. Do you want to show her the best anime of all time or do you want to show her an anime that will get her watching anime. Because if you want her to watch anime regularly then you need to find out what types of genres she's into, romance, comedy, action, horror and so on. and then based off that information find the best anime in that specific genre to get her to watch.

Um exactly what type of genre do you think she would be interested in? There isn’t exactly a best anime, everybody has diff taste and opinions. Here are some recs

Romance or Rom-Coms: Fruits Basket, Ouran High School Host Club, Toradora, Darling In The Franks, Guilty Crown, Plastic Memories, Maid-sama, Horimiya, Love is War, Kiss Him Not Me, Ao Haru Ride, My Love Story

Psychological or Horror: Death Parade, Death Note, Erased, Psycho pass, Zankyou no Terror, Mirai Nikki, High School Of The Dead

Slice of Life: Anohana, Clannad, From Me To You, Disastrous life of Saiki K, Love Chunibyo and Other Delusions, Beyond The Boundary, K-on, Himouto, Umaru-chan, Given

Some others: Violet Evergarden, Angel Beats, Banana Fish, Fairy Tail, Danganronpa, Orange, Your Lie In April, Your Name, Children of The Whale, Vampire Knights, Erased

Best Starter Anime in my opening is Erased or Ouran High School Host Club, but if she wants smth more thrilling, let her watch Death Note or Mirai Nikki. Heck, if she doesn’t mind the fanservice, let her watch High Rise-Invasion. It’s a pretty good anime, just the fan service is a bit to much.

Your Lie in April: a romantic tragedy and it's fairly short.

Shreck the musical. 

Try the slice of life genre of anime, such as "Train Man" and "The Wind Rises".  

as they said, it depends on the genre that she is into with regular shows.  take a look at the shows she actually watches that are not anime, and  then  ask the question again , what is the best anime that are like   --- these shows  -- etc

death parade is really good anime!

Pokemon!!!!!!!!!!!!!!!!!!!!

Since anime is just a medium, there is no "perfect" show. It depends on the genre(s) she is interested in.

Some titles I think might serve as a decent introduction are:

* Baccano

* Claymore

* Ghost Hunt

* Haibane Renmei

* Moribito

* Now and Then, Here and There

* Orange

* Paranoia Agent

* Shinsekai yori

Generally speaking, they avoid comedy and over-the-top superpowers or character archetypes like tsundere/kuudere. Things that might be off-putting or lead to generalizing anime as "stupid" by people who aren't into that kind of thing.  

Robotech