As far as Netflix goes Fullmetal Alchemist Brotherhood is very much worth your time, and one of the few examples imo where the dub is actually better than the subtitled version for voice acting.
Death Note is woefully misogynistic but quite good fun (for the first half at least) if you can get past that. (let’s be honest, if you can’t get past it at all anime is going to be difficult)
As far as things not on Netflix that you may be able to source by one means or another (including Netflix in other countries)…
Natsume’s Book of Friends is my absolute favourite series. It’s a very gentle and kindhearted episodic series about a boy who can see yokai. Makes me feel very warm and fuzzy inside (although can also be very sad). Beautiful soundtrack. Think it would be flat out impossible to dislike it.
Mushishi is story of similar to the above in that it’s based on Japanese folklore, but it’s more serious.
Kino’s Journey probably fits broadly into the type above, and is about a girl who travels to very different, quite messed up, places. Again despite dark themes it’s a pretty gentle watch.
For something very different to the above, try Baccano. It’s a completely absurd series about immortal people in early twentieth century New York. Grotesquely violent, time line hops about constantly, utterly mad, but quite good fun and another one which is better to watch the dubbed version.
I remember liking Gankutsuou (a very odd adaptation of The Count of Monte Cristo) at the time, but I never rewatched it so don’t hold me to it being good.
