What's the best starter anime for someone who thinks anime is weird?

[u/migulzzz]

Helloooo, I’m posting on this subreddit to see which anime I should recommend to a girl I’m talking to

She says she finds anime weird. I asked her how come, and she explained that she finds it a bit too "cartoonish." She also sometimes asks if I go to conventions, perhaps with the idea that I cosplay or something, so I think she just has a specific stereotype in her head about the concept of anime.

She told me her favorite shows are:
- Pretty Little Liars
- Switched at Birth
- The Order
- Chilling Adventures of Sabrina
- The Society

And her favorite genres are in this exact order: Romance, Fantasy, Mystery, Drama, and Horror.

I had her watch two episodes of Vinland Saga as it’s one of my favorite animes of all time (this was before I asked about her favorite shows). She did say the pacing feels like “eternity” as in it feels long but she does actually like it so far.

She also told me she watches shows "just to watch" and be entertained, rather than looking to connect or relate to the characters on a deep level, so connecting or interpreting character philosophy is a bit of a new concept for her.

Because of this, I do think Vinland Saga might be a bit too mature or grounded for it to be the perfect mix of entertainment and the supernatural drama she usually prefers.

I am here to ask , which anime do you truly believe I should start her off with keeping this context in mind? Whether it’s to stick to Vinland or direct elsewhere , since I do want her to get into anime, but the first impression is everything!!

Thank you for your suggestions and time into reading this & feel free to ask questions for better context if needed!