I would recommend Princess Tutu but that would ruin anime to a newcomer as that's peak quality.
If you want introductory shit try Madoka, it's a wild ride for people that want to pop their anime cherry as it introduces you to Genism and Shaft animation being trippy, it can also make you interested in 3 genres if you want to see where the inspirations for it come from.
If you want a softer ride there's Patlabor as a round to earth take on mecha with character focus, it being so down to earth will get you hyped for the rest of the genre and its a great introduction to early 90s late 80s anime as there are recurring themes splashed among them that you will find all around.
Kekkaishi is a great introduction to Shounen mystical themes and even into Manga if you want to see the wild ride unfold.
There's around 50 shows every season so you could hop on and enjoy 12 weeks of hype and random bullshit too, new season just started so you could just pick a random one that isn't a continuation if you feel bold.