My personal rec for watching HxH is go with the 99 version until the end of the first OVA (the end of Yorkshin, in other words), then pick back up with the 11 version from there (episode, like, 58 or 59, I think?). The overall debate of 99 vs 11 is a whole thing unto itself, but I thought the Greed Island OVAs that came after the 99 TV run suffered a fair bit from being seperate productions (fair bit of typical early digital issues in the GI OVAs in particular). This is also pretty subjective but I really feel like 11 overall got better as it went, and that GI was the point it started hitting its stride. A lot of the early arcs in 11 felt almost phoned in compared to ones after, and they just flat out didn't nail the tone of Yorkshin as well as the 99/OVA did. On the flipside, while the older OVAs for Greed Island included a few of the bits of flavor from the manga that was cut in 11, overall it's just a poorer adaptation. It could be kind of jarring switching from the old set of adaptations to the new, but you'd have to at the end of GI anyway if you were going to continue.
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I think the 'anti-genre' behavior you ascribe to elitism is not really so. An elitist, to me, would be someone who disregards completely the tastes or opinions of anyone considered unworthy by them. This doesn't really mesh with wanting to be seen by the general public as more sophisticated or legitimate. When I've seen people say things along the lines of 'fanservice/ecchi/harems/action shounens/isekais/whatever are dragging the reputation of anime through the mud', it strikes me as almost more an inferiority complex about their hobby and desire for they themselves to be seen in a better light moreso than a comment on the content itself.
In reality of course, the world at large doesn't generally care about someone's hobby so seeking validation for it is (ironically, in this case) kind of childish. Simply watching what you enjoy will always lead you the best way regardless of whether that's appreciating thematic depth or a nice pair of tits (or both).
It's all too common an issue when watching OVA series, but there's still not many I'm as sad about sudden cut-offs to than this one. I liked it the most out of all Shinbou's early work I've seen, it's got such a great blend of genre parody, mecha, ecchi and high energy. Really surprised anyone else here cared about it enough to make a thread, though.
It really depends on what level you want to play at, I think. Kei is certainly 100% tomboy and if that's what you're into that's what you'll get, no pretensions. On the other hand Yuri is only acting the part of the ditz in order to work that appeal. If you went for her only wanting the 'cute, girlish' type of girl you'd eventually be disappointed, but I think the appeal of Yuri is appreciating both the act she puts on, and the 'real' tomboy underneath. As for their sense of professionalism that seems to vary based on the plot's demands anyway, so I wouldn't hold it much against them.
This isn't directly related but I thought about it before: there can't really be that many chances for them to sustain a relationship very long. When you take the pool of men they'd be interested in, and narrow that down to only the ones who don't mind their reputation (few, from what you see in-series, and I'm pretty sure there's a few times they get dumped when the guy realizes what he's gotten into), then further down to ones that would put up with the absurd time and travel demands on them from their job, there'd be practically no one left. Even more than their disposition this might be why you see them burning through boyfriends and why the two of them seem almost constantly thirsty.
The arc itself it an extremely drawn-out, twist-heavy game played over one night. It felt appropriate afterwards that that's how I read it too, but it just kinda happened that way. It must've been agonizing for people following as it came out though, almost 20 years of real time publication (no Berserk/HxH-tier haituses either) that only covered 1 night in-series.