ALMOST anything by Naoki Urasawa. Homunculus was weird af but in a good way and, of course, Fullmetal Alchemist.

Watashitachi no Shiawase na Jikan would prolly be my top one or two (against FMA) -- this manga literally broke me. SAIKANO AS WELL omg.

Best artist for me would be Irie Aki followed by Soon Ki, Konishi Asuka, and Rumiki Takahashi's earlier works.

I find picking the 'best story' really hard because of how subjective and transient my preferences can be. Regardless, I believe Fullmetal Alchemist is the quintessential manga. I can't say it's my favorite but I honestly think that it sets a gold standard especially for shonen.

As for art, perhaps Takehiko Inoue, Kaoru Mori, and Inio Asano, but oddly enough I like Yusuke Murata the best not because I find his art good (and it is) but because I appreciate his work on titles that he didn't author. I like how he adapts to what he's working on without losing his signature.

I think anything by Hikawa Kyouko is fantastic, in both the art and storytelling departments. She's got a very clean, simple style, and her stories are lighthearted and often focus on the importance of platonic relationships. Kanata Kara is my favorite of her works. I also really like Eyeshield 21, by Inagaki Riichiro and Murata Yuusuke, which has a large, eccentric cast, fabulous art, and compelling writing. I like One Piece for similar reasons.

For story, probably Nijigahara Holograph, Uncivilized Planet, River's Edge, Hachimitsu to Clover... I could keep listing here though.

For art, I think Kataoka Jinsei would be my favourite, though I wasn't too impressed by the story of the manga of his I read.

Oh definitely Black Haze for art. Ironically, the art in the beginning is absolutely terrible, but it goes on to be some of the most jaw-dropping art I've ever seen in a manga. To you the Immortal is also fantastic in art.

As for the best story, I may have to say Homunculus. Although completely insane, the story is solid and the characters feel real. Every character has real flaws and its really great.

Otoyomegatari

It's both beautiful and the story is really interesting. I suggest you look at it even if you aren't going to read it. Its art style is goals tbh.

Putting Otoyomegatari aside, for me, the best stories (they also have beautiful art) are those by CLAMP (all of the stories lol). They have a variety of different kinds of manga (from really fluffy to really sad) but they're all deep and beautiful in their own way. I love how CLAMP can take a heartwarming/funny story and turn it into a tragedy. Besides CLAMP, Tamura Yumi makes some manga with amazing stories. Really original and complex. However her art style is a little old (even in her more recent manga) so there's always mixed opinions regarding that. Personally, I like it.

I also thought Sheryl: Kiss in the Galaxy, and Macross Frontier had pretty good art styles. Sheryl is beautiful in both.

Btw, I love Kanata Kara, Eyeshield 21, and One Piece (these were mentioned by @bioluminonsense). If you haven't read those and are looking for some good manga then I totally recommend you those.

Best art is Berserk, hands down. You can feel the craftsmanship from every panel, and the artist is really good about implementing opposing styles/emotions (For instance, chibi super-deformed fairies in a dark fantasy setting). Storywise, the golden age arc of Beserk has extremely good storytelling, and the arcs before and after it are good, but after that the story is kind of a mess with too many characters. The art never disappoints, though.

Well, my favorites are Konno Kita, Tono, and Funato Akari. They're really the first ones who come to mind when I think of perfect combinations of art + story.

Kui Ryoko is great too, as is Tsubana, for fantastic art coupled with super inventive stories.

Oh, and I love Toume Kei's art, but I range from burning love to mild disinterest in regard to her stories.

As for specific manga, Gisèle Alain, Mahoutsukai no Yome, and Cesare come immediately to mind.

Art definitely has to be Golden Change for me. It's beautiful.
Also, I think art by Yamamori Mika is neat and pretty too. Two of her very famous works are Hirunaka no Ryuusei and Tsubaki Chou Lonely Planet.

MOCHIZUKI Jun and Tobasco Yana draw amazingly beautiful art. I just want to stare at their manga covers for ages.

Nulla in mundo pax sincera
"Always go too far, because that's where you'll find the truth." - Albert Camus

Good art:

Chang ge Xing - Absolutely gorgeous Chinese artist. Gorgeous is the best way I can put it.

Tomodachi no Hanashi - Breezy, thin lines and a very pretty style.

Shouwa Genroku Rakugo Shinjuu - Simple, clean art. This manga isn't BL but the mangaka is a BL artist it looks like. BL artists always draw guys so well :'|

Koiiji - The art is very clean and I like the style.

Best stories:
Kubera
Chang Ge Xing, which also has amazing art.

Both stories are relatively complex, with a lot of characters who follow their own agendas. Chang Ge Xing's strongest point would be its brilliant female lead, while Kubera is best at showing the relationships between characters, their struggles, and how they change over time.