I believe the best starter animes must need some criteria:

• not too long (seeing something having hundreds of episodes is a huge hurdle)
• self-contained (no spin-offs of other franchises that you need to know)
• completed (no “if you want to know how it ends you have to read the source material or hope for a second season”)
• no need to know cultural references (what the fuck is a shikigami?!)
• universal themes (love, hate, friendship, hardship, etc… Stuff that applies to everyone)
• characters should be likable (no one keeps watching if they dislike the characters)
• interesting from the start (no “uh, it gets great from the 5th episode, just keep at it”)
• interesting throughout (show shouldn’t fizzle out or run out of steam)
• normal visuals (yes, shows with unique art styles can feel fresh for someone with more than 1000 shows under their belt, but for a new watcher better keep it normal)
• not mundane but not too far “out there” (just the right amount of fantastical)
• it should end on a positive note (I wouldn’t have touched another anime ever again if Grave of the Fireflies were my first one)

With all those criteria listed, I believe the best show that ticks all the checkmarks is Anohana: The Flower We Saw That Day.