The stories were rearranged and released in an optimal rather than chronological order. Sometimes this will create some problems for the story, but it will make the story more optimal as the manga wasn't exactly released with a lot of the continuity in mind, but rather some of Tezuka's random ideas. The manga itself started as a horror manga, rather than a drama, so it also helps establish the drama side better.
Back to what I said about drama, some of the chapters nail their drama really well do this really well, but some really fail on it, ending up as silly instead. I assume it's because Tezuka tried to be overlydramatic and illustrate his point through too many coincidental events in the stories or he simply had an idea but he was pressed on time and couldn't come up with any better idea or couldn't hold up well with it. Sometimes you'll even found repeated themes. I think as a result of the fact that at times he tried to take the manga too seriously, he sometimes likes to get the manga to break the fourth wall, either through his own characters or by including himself in the manga.
As for the questionable content I specified earlier, it's pretty much a result of aging. I'll say that some things were different back then and just leave it at that. It's pretty much things you would expect which I doubt could be found offensive, at best you'll find silly, except maybe for the chapters that were removed from the volumes for questionable content themselves. Which I couldn't find and I've heard that they are only in japanese, so, if you know japanese, you might have better luck unraveling exactly what's the peak for questionable content.
Overall the story goes in a lot of places and it can best be summed up as a collection of the more notable stories of the unlicensed surgeon Black Jack. As it goes into a wide variety of themes, the best way I can describe the story is dramatic, as most of the stories are that or are aspiring to be dramatic. Also keep in mind that the story is a collection of stories about Black Jack, so don't expect the manga to have a conclusive ending and be more than just a collection of stories.
The art style is from when manga took great western influences but, for instance, the surgical parts of it are drawn in a moredetailed style, so if you're afraid if there's anything medical that would suffer as a result of the art, do not worry a bit, it won't. If art style is not a big yiff for you but you still dislike it, keep in mind that the overall style of manga was under development. So if you don't generally care much about the art, don't weigh too much on Black Jack's. At the time there wasn't much differentiation in between art styles.
Now, character wise, there's not a whole lot of characters to talk about, as some even if recurring won't be memorable, while some will be. The most developed character in the story is Black Jack, of who's development is best shown inside the chapters themselves, but just in case you might have the wrong idea of what kind of character Black Jack is, he is a medical genius which does not own a medical license, who will operate on you only if you can meet his outrageously high demands. While he does value money, quite a lot, he also does value honesty and integrity and he shows that through his work. There are plenty of layers to Black Jack's character. So don't lose sight of that. Talking about any other characters would be spoilery, but note that they generally aren't bad. They usually are means to an end but some of the recurring characters will be interesting. Just don't expect TOO much from them. Most of the focus is on Black Jack & the drama surrounding his operations and real issues of the time that do apply even today, to some extent.
The stories are very enjoyable even when they don't achieve the purpose they try to set for themselves and what I mentioned as questionable only ends up as silly at best, by no means offensive or disturbing. If you're ever in the mood for a bunch of short stories that travel a great deal of themes, Black Jack is a good choice.
