Anime The manga: A flawed but interesting adaptation
The other reviews focused on the anime, and I don't have much to say apart from how Girls und Panzer is a show that is well worth your time. This review deals with the manga, and the question of whether the same can be said for it.
The story is essentially the same as Girls und Panzer, although it's told from the POV of Yukari, rather than Miho. As a result, some crucial scenes are omitted or changed, whether the result of Yukari not seeing them (for example, Miho coming to Oarai and deciding to do tankery), or various other reasons, (for example, the first round shown is the second match with Anzio, rather than the first match with Saunders). As such, it's best if you already know the story before reading the manga.
Unfortunately, Yukari is largely a less interesting character than Miho, having fewer meaningful interactions with others. It's nice to see her thoughts, but it's unfortunate that most of them boil down to "I've got to support Nishizumi-dono!" The rest of the Anglerfish crew gets Demoted to Extra, and develop far less over the course of the story. Oddly enough, even Yukari's own family isn't shown much, nor is her backstory expanded on apart from the part about her having no friends until she met Anglerfish Team. As such, I'm not entirely sure why Yukari was chosen as the protagonist apart from her popularity, but Miho would have worked better as the protagonist.
There's a fair amount of information in the manga that can be quite interesting, shedding light on the tanks' capabilities, and on certain characters' actions. Unfortunately, the exposition can be ham-fisted at times, and tends to eschew the anime's tendency to Show, Don't Tell. For example, we're told about the nature of Sodoko and Mako's relationship, rather than shown it.
Of course, this isn't to say that all the changes are bad. Some things are better explained than in the anime. Without spoiling anything, there's a change to Miho's backstory later on that provides an interesting possibility of why she was affected so much by the events of the previous year. While the manga is largely non-canon, especially after the Anzio OVA, it's interesting material for fans, especially fanfic writers.
As an adaptation of Girls und Panzer, the manga has its flaws, but it's worth checking out if you're a fan of Girls und Panzer.
Anime Cautiously Optimistic
The first season of Girls und Panzer is a welcome twist for anime, in that it's all-girl cast doesn't have to stoop to cheap tricks like constant fanservice of yuri storylines to keep the viewer interested. The interpersonal relationships do mirror those in real life, from the personalities of the freshmen girls (Ask any rookie sports player and they will admit they get nerves) to the fascinating quirks of the team (History club comes to mind) and how their opponents define the girls of Ōarai in their quest for the championship. The OV As similarly do a good job of painting a more lighthearted picture, and since there's no real plotline to worry about, the fanservice does increase, but not to the point of ludicrousness (OVA 1's swimsuits as covered wall to wall in brilliant references combined with the personal tastes of each girl), which can be okay given the lack of a real plotline. What really hooks you are the bonuses you get from rewatching, as each girl's personalities and the sport itself benefit from multiple rewatches and realizations on what you might have missed the first time.
What is worrying is how the creative team can keep this up for the next season and movie. Personally, there is a fear that the show might make some major missteps for the next tournament arc, and might even fail the Bechdel test it so beautifully passed in the first season. While character growth from season to season is expected, going too far out of character could turn Gu P into a self-parody too early.
Some might deride the supplementary moments in the show as ludicrous, but after series about vampires fighting for England, alchemy in war, and vampire high schools, the idea that high school girls in tanks riding around on massive city ships is sharply put into perspective.
Girls und Panzer definitely has a good hook and keeps the viewer interested, but if they want to keep their streak, they need to stay loyal to what makes the show unique, and avoid the pitfalls that other "Schoolgirl war stories" fall into.
Anime As much fun as it sounds
GuP is obviously a show in which plot follows premise. The story itself is "classic sports movie": our heroine, Miho, a reluctant former tankist, must get back in her groove and lead her Ragtag Bunch of Misfits to victory against the haughty champions or her school will be closed. The creators will get no prizes for originality; what they do will prizes for, however, is creating great characters. The protagonists are rounded, three-dimensional, and believable. Even minor characters are more than mooks; the tournament is a window on their lives as much as it is Miho's trial - as the many ensemble darkhorses attest. My favourite was Kei, leader of the "American" tank team, and Cavalier Competitor. The viewer will find plenty of people to root for.
When we turn to the panzers, we find similar quality. The level of detail is enormous, but, helpfully, Yukari will keep non militaria geeks informed. Each tank is lovingly - and beautifully - drawn and rendered. There's a wide selection - KV-2s, Shermans, an almost-useless Type-89, and lesser-known tanks like the Jagdtiger all make appearances. Then there's the little details, like the screens the spectators watch, built on Krupp K5 railway gun chassis. The setting does require some suspension of disbelief, but this is easily given; when the show began I wanted to know exactly why schools in the GuP universe are built on giant aircraft carriers. When it ended, I still wanted to know, but this time it was because I wanted to explore the setting further.
Some might feel political analyses of a show like this are unwarranted, if that's you, then skip this paragraph. The setting is handled deftly - no, beautifully. A show where tank combat is a school sport might attract accusations of militarism or conservatism. Neither element is present; indeed, the effect of the show is not to glorify war, but to sanitize it into nothingness, in much the same way children play at pirates. Nor is the show markedly sexist as some seinen-timeslot anime can be; the creator is notably puritan, and GuP does not so much pass The Bechdel Test as obliterate it with a 75mm gun.
All in all, it's fun, funny, and exciting. Dive in - you won't regret it.
Anime Anime Season 1
Having watched the anime, read the various spinoff manga and seen the movie, I feel it's time to do a review of the series in retrospective. I'm no longer quite as enamored with it as I once was, so I'm more easily able to see flaws, but I still think it's well done and worth your time.
The plot is fairly standard high school sports fare (and thus somewhat predictable), with a girl rediscovering the love of her sport and leading her underdog team to victory... except the sport is tank combat and the high schools are all on giant carrier ships. The setting is surprisingly well thought-out, even if a lot of the relevant information about it is in supplemental materials.
The mainstay of the series is tank combat, which provides a nice mix of strategic planning and intense shootouts between the tanks. The fact that victory's decided by whoever takes out the enemy flag tank first helps keep things suspenseful, by allowing the protagonists a way to come back from an overwhelming disadvantage, and their rivals a way to defeat them at any time.
Oarai's tankery club members are a diverse bunch, as are their opponents, but the cast is spread somewhat thin over 12 episodes, and there isn't time to develop them all, resulting in some tanks having three to six people with virtually identical personalities. The main cast is somewhat better developed, but occasionally, the writers tend to fall back on their dominant characteristics and forget about their Hidden Depths. Some characters are highly underutilized, such as Maho, who's Miho's older sister and the leader of her strongest opponent (as well as Miho's former school). The sisters' relationship is more interesting and loving than one would initially expect, but, unfortunately, that's one more detail that isn't shown much in the anime, instead saved for Little Army, a prequel manga.
The soundtrack features quite a few fitting songs for the various competitors from their various nations, such as Panzerlied, which nicely fit the action and the many World War II references. On a somewhat related note, people with an extensive knowledge of WWII (history majors or people who enjoy reading about WWII as a hobby) will get more out of it than those who don't know much more about WWII than what they learned in school.
All in all, GuP is far from perfect, particularly as far as characters go, but it's still an entertaining and original series that's worth a view.