JoJo's Bizarre Adventure, Vols. 1–3
The original story came from manga, so I can't fault the anime for glaring holes in the story logic. Mind you, the third disc says this is a prequel, so I'm not so sure that excuse still applies...
The basic story sees Joseph Joestar coming to rescue his grandson Jotaro from prison. Jotaro thinks he is possessed by an evil spirit. In reality, he has the powers of an astral spirit in his control, an ability called a Stand.
In the second adventure, his Stand earns a name (Star Platinum), and an assassin sent to eliminate him and his grandfather becomes an ally instead. In the third adventure, another hired assassin joins them. That seems to make the entire team, as no other assassins join them in the second disc. They now become a group of five (grandfather Joseph/Hermit Purple, his Indian aid Avdol/Magician's Red, Jotaro/Star Platinum, Noriaki Kakyoin/Hierophant Green and Jean Pierre Polnareff/Silver Chariot), with the intent to kill a vampire who has plagued the Joestar family for 100 years, Dio.
An interesting thing about Stands: they don't all appear as humanoid beings. Hermit Purple appears as a set of vines around Joseph Joestar's hand, and provides psychic visions. Another appears as a gun in the second disc, and as a mist in the third.
There is another element of the series: this is the third of a generational character set. Four Joestars have fought different evils. This JoJo is the third one in the manga.
This series is equal parts gothic horror, fighting manga like Fist of the North Star, and the superheroics of Marvel Comics. As a series, it has developed a cult following—smaller than that of Dragon Ball, but still a good sized following.