Where should I start with this? The good in the story? The bad? The average? What the arcs are, and which ones are important and not important?

I'll start with simply assuming that people know of the first two manga. If you haven't, then it is a must before reading the third part. You cannot go into this manga with no backstory or background information and expect everything to be clear and satisfying in the end.

Also, spoilers. I'll even give a few warnings as to what to expect for those that are more 'sensitive'.

This manga has "4" arcs to it. Or, maybe I should say, 3 major arcs and a mini-arc to the side.

The first arc is a mix of three things: Good, forgettable, and could have been cut shorter. How is it possible for these three to exist in one? Well, here we go. Long story short, Baki tries to get into the same prison as Biscuit. How? I'll leave it for you as a surprise to find out. Bottom line is that he wants to fight and beat him before facing his father. Between his entrance to the prison and the fight, everything could have been cut out. We finally meet Biscuit's girlfriend, so she can stay. But everybody else except for Baki, the girlfriend and Biscuit, can go to the land of nonexistence and forgetfulness. None of these characters show up again, after this arc. To be fair, the girlfriend doesn't either, but at least she's important to Biscuit's identity. Anyways, these characters felt like they were holding this whole arc back and dragging it as it tried to get a move on to the fight. There were a few "important" characters in there, but they're forgettable. There were also a few mini fights, even between one of these "important" characters and Biscuit, but it can be cut out. Though, you may enjoy it for the simple fact that it's a typical fight of this franchise. But that's about it. This arc is important, so it's a must read. My suggestion is to skip to the fight between Baki and Biscuit and just move on from there.

The second arc is the most amazing part of the story. It is the typical "what will happen if a prehistoric man was brought into present day?" story. Pickle (the prehistoric man), has lived in the time of the dinosaurs. He has devoured them and was stronger than them. You will have to leave common sense, history and science at the door for this arc. What's great about this is not how Pickle handles modern day, but his interaction with the martial artists/fighters of the franchise. Also, how he develops as an individual through fighting them. The reasons behind his actions makes sense and they are explained thoroughly in this arc. This is something that you can appreciate as a reader, because it gives you a connection to Pickle. Before Baki, he fights 3 others, 2 of who have major life changes as the aftermath. Warning: there is cannibalism and a bit of sexual assault in this arc. No rape though. But this arc is heavy with psychology and what makes a human, a human being. You can't help but feel attached to Pickle. The author does well to tell us how he feels and thinks without the means of talking. Though, they give you a bit of a surprise about that in the end of his arc. If not for Pickle, Baki would not have had obtained certain skills to fight with his father in the end. I was rather sad that the arc has ended when it did, but I cannot say that I left disappointed. The ending for it will leave you either frustrated, happy or with a bittersweet taste. Overall, you cannot skip this arc by any means. You must take your time to read through it, as it will not leave you disappointed.

The third arc is forgettable. That's the best way to describe it. It makes the first arc looks like this great adventure (which it wasn't). Retsu wants to learn how to box. Why? Hell if I know. This mini arc is so short that the fourth arc keeps on barging in, and I was more interested in the final arc than the mini one. I love Retsu to bits, but even the characters themselves admitted that it didn't make any sense and decided to leave him to his devices. What's rather insulting to the sport is that he still uses his kung fu stands in boxing matches. I don't know the rules for boxing, and anime/manga always throw common sense out of the window, but it is safe to ask this: where is the common sense in this one? Why would Retsu go out of his way to learn how to box and even leave Japan to fight oversees, if he continues to use kung fu on some level? He is so out of character that it's frustrating to read. Overall, you can skip this arc, but I suggest a different tactic. Ignore Retsu's "journey" and read through the fourth arc when it pushes itself into the story. It has absolutely no impact on the story overall.

The official fourth arc is where Baki finally fights his father. The fight goes well over 50 chapters, but the arc doesn't stop with it. Instead, it starts with Yujiro finally admitting that he loves his son. He accepts Baki's invitation for dinner, they eat together first at Baki's old place and then at Yujiro's chosen location. Then the fight starts. This is where the satisfaction comes in, if you read the first two manga. The psychology and interaction between the two will leave you on the edge of your seat, breathless and in awe. Personally, I cannot wait to see it be animated, one day. Finally, after so long, the story comes at a full circle. The fight itself is not just a fight. It is a psychology and relationship between the two as Hanma members, father and son, and two fighters are talked through here via fists, words and memories. There are even 'touching moments' between them as a father and son. If you see the actions as 'touching', anyways. Yujiro's father even makes an appearance for a brief few chapters. Depending on the type of fights you enjoy and what satisfies you in the end, this fight will, again, leave you in three states: pleased, frustrated or bittersweet. If you want to, you can push in there anti-climatic. Overall, this arc is a MUST to read.

I enjoyed this a lot. This is a manga that I would definitely re-read in the future. It is unbelievable, gives us something fresh and new, and gives a long-waiting story its proper ending. I simply cannot wait to read the fourth manga. But I'm still a bit disappointed with the first and third arcs. They could have been dealt with better, or taken out altogether (and I'm looking at you third arc). But in the end of the day, I highly suggest this franchise to anybody and everybody. If you have read the first two manga and don't know if to continue, I recommend that you do. You can use this third manga as "the end" of the story, if you don't want to continue any further. There's no shame in that. After so long, as I said before, the story came into a full circle.