Here are some titles that have worked brilliantly with Year 5 and 6 readers: Cardcaptor Sakura and Angelic Layer (CLAMP) - Kitchen Princess - Pokemon - Moyoco Anno's Sugar Sugar Rune (alas difficult to get hold of) - One Piece - and Sugar Princess (about ice skating) by Hisaya Nakajo (best known for Hana Kimi).
Hope those titles help! (btw these manga were read avidly by both boys and girls),
I think Sarah has made some great suggestions and a few I would have said myself. My own suggestions would be Yo-Kai Watch (very similar to Pokémon, in fact Viz are pegging it as the next Pokémon for them) and if your niece is into sports at all then maybe you could show her Haikyu!! or Kuroko's Basketball. For something a bit more 'girly' there is the likes of Ouran High School Host Club which is pretty harmless from what I remember... I also like Maid-Sama! especially now Viz are publishing it as 2-in-1's.
A lot of the shonen jump titles should be suitable provided they're more slice of life/sport types of the genre... I want to suggest Naruto but I think that's too violent early on and Sarah's suggestion of One Piece is better out of the big shonen on offer. Definitely try and get her into Fullmetal Alchemist in a couple of years though!
If she becomes interested in manga in general maybe get her into Bakuman as well? It's a little more complex than the other suggestions and quite wordy but I adore it for what it taught me about the medium and how it's created, at least within the context of being a Shonen Jump title.
*edit* Just remembered that Viz publish The Legend of Zelda manga, for a fantasy adventure series those are really good and generally self-contained stories to a single volume or at most two so won't be costing the earth for her/family to keep up with. She could just pick and choose whatever story caught her eye
Cardcaptor Sakura would definitely be a good shout. Maybe Sweetness & Lightning?
I remember personally Sailor Moon kinda surprised me - it's definitely pretty dark in places, with character deaths and the depiction of its villains. One of the characters also has sex (although it doesn't show anything graphically)