I'm not an anime fan, but I want to get into it, and I'm looking for something that meets my specifications.

Ayyy, try out Hunter x Hunter (2011). Be warned though that it'll kind of spoil every other fighting series out there for you.

Try cowboy bebop

Steins;Gate is most definitely my most favorite anime of all time. the art may not be something special, but it has a unique world, great characters, and an amazing story. it starts off slow and you may be tempted to drop it, but i implore you not to. it's ranked #3 on myanimelist.com for a reason.

Parasyte is also one of my more favorite shows. it builds a pretty in-depth world and has one of the best character development i've ever seen. some of the side characters feel pretty flat and two-dimensional, but they all serve to help our main character change and evolve. and it's got some pretty good animation to boot. this show isn't afraid of blood and death though, so be prepared for that.

Death Parade used to be my most favorite anime until i saw steins;gate. the world is wonderfully crafted with one of the most unique settings i've ever seen. the characters all feel fleshed out and don't really fit into any stereotypes or cookie cutter molds. the art is great and has one of my more favorite OPs

Shinsekai Yori. i personally didn't like shinsekai yori, but most people seem to love it. regardless of how i liked it overall, i have to give shinsekai yori credit for having THE BEST world building i've ever seen in anything. the world the creators made felt alive. it felt less like i was watching a show, and more like i was peering into history.

Have you tried Kara no Kyoukai?

I was going to suggest Ghost in the Shell, but the Major can be a bit of a Mary Sue at times. Secret organization Section 9 invistages cyber crimes and cyber criminals.

Cowboy Bebop, if you like the classic anime art style this show is a must. Strong fleshed out characters, well fleshed out universe. Wonderful mix of space, jazz, and a western feel. Only down side is that it does have a bit of fan service but it is not the crux of the show in anyway.

Berserk (1997) While i don't have an opinion on the current running Berserk, the 1997 version is solid gold. Good character and world building, even if Guts, the main protagonist, is more than a little OP. Fantasy mid evil setting with lots of blood and guts. It has a bit of man service and fan service but again neither is a big part of the show. It is one of the few examples of an anime having bloopers as a bonus.

Steins;Gate. Time travel science fiction story. Good characters, good world building. Does lean a bit to the Harem side because of the original source material but it isn't a major driving force of the anime.

Spice and Wolf. Bit of a dry anime....Story of a traveling merchant befriending a wolf goddess and gets drawn into helping her return home to the north. Not a lot of action here but very focused on characters and the world around them. Pretty hevy helping of fan service with this one though.

Madoka Magica, Don't let the cute moe look fool you. This magical girl show is far darker than you might think.....

I will never, ever, ever stop championing {Mononoke} everywhere it's relevant. It hits every single bullet in your list. from the consistent world building to the striking visuals to the avoidance of traditional anime tropes such as fan service and haremshit. It's one of only two 10 rated shows in my entire MAL. No one should miss out on this masterpiece.

I would recommend watching some Studio Ghibli films if you haven't seen them, especially {Spirited Away}.

I'll also recommend

{Denpa Teki na Kanojo}

{Psycho-Pass}

{Eve no Jikan}

{Zankyou no Terror}

{Haibane Renmei}

{Zetsuen no Tempest}

For Complex characters & Strong Visual Aesthetics I would honestly suggest: {Psycho Pass}

The Ability for the writers of this show to present these characters that are described as one dimensional and for the story to develop and they become more complex is amazing in my opinion. The animation is fairly new looking so there are some scenes that are really beautiful and the story is actually very intricate. Not REAL spoilers but if you wanna read up on it yourself:[] (#s "Futuristic world where the "police" have technology so advance they can stop a criminal before doing anything and using latent criminals to help them stopped the crimes from being commiteed") and the story keeps a lot deeper the farther in the story you go.

Another GREAT anime that might peek your interest is {Darker Than Black}

This anime literally started my long overdue addiction to anime. The show is good subbed and dubbed depending on what you watch. [] (#s "everyone in the world is living a normal life yet there are special "hitman" that can be hired and signed by contract to kill other humans. These "contracts" once signed have to fulfill their contract yet every time they complete a contract they have consequences they have to pay. the MC is one of these people who go after other contractors to prevent the murders") It is actuall a very stick to your skin kind of story and this is EASILY binge watchable.

These dont really cover the flash fighting but they are amazing none the less.I have a few other anime's but unfortunately I have to return to work. If these peek your interest message me and I will give you some more.

• {Tokyo Ghoul}; it's pretty good. "Weak" MC; well done world.
• {Log Horizon}; and the world is beautifully built for those who aren't familiar with MMORPGs. There is a tiny bit of fanservice but not much.
• {Psycho Pass}; brilliant- while the second season falls short (imo)
• {Berserk}; the first series is gold. Haven't seen the currency airing one. Granted the visuals aren't too great, given its age.
• {Darker Than Black}
• {Future Diary}; a bit of fanservice; interesting characters; Every. Fight. Matters.

Just a general tip, follow the 3 episode rule. If you think a show looks interesting, watch the first 3 episodes and see if it grabs your attention. If you don't like it, don't force yourself to watch it, just move on to the next show. Just getting started try to pick things that have an MAL score over 8 and that you think have an interesting premise.

You've gotten lots of great suggestions so far, but I'll throw a few more out there that I liked and think are accessible.

Samurai Champloo (MCs are super strong, but the focus is on the world around them)

ERASED

Also Steins;Gate and Cowboy Bebop have already been suggested and are 2 of my all time favorites. Bebop is the show that got me into anime.

I would recommend {Full Metal Alchemist} and {Full Metal Alchemist: Brotherhood} . FMA has a different ending than the manga so the creation of brotherhood was made to appease fans who wanted the manga ending. One of the top rated animes and it's really awesome. I'd probably recommend this to anyone wanting to try anime out

Maybe {Fate/Stay Night: Unlimited Blade Works}

Great animation Absolutely orgasmic animation, good characters, understandable(at least to me)

There's great suggestions here, but I would like to add the following:

{Hai to gensou no grimgar} The art is just gorgeous. The story is quite slow, the fights are not a main part of the story, since most of the time the anime tries to build solid characters that have distinct personalities, as well as clear world building. I wouldn't say the world building is the best, but it is decent. The fight scenes in this one tend to affect the story flow as well. Favorite part of the anime is definitely the art. Many ppl complained abt the pace of the show, but the slow progress of the story helped me appreciate and take in the amount of effort that was placed in the art and drawings.

{seirei no moribito} The art is this one is definitely unique, and the lines are bold in the drawings. The animation is very fluid, and the fight scenes are beautiful. The world building and character development is great and in depth as well. My favorite part of the animation is the characters, and it feels like I was part of the entire journey as the story developed.