If you didn't like the story of "Lord of the Flies" there is a good chance you won't like this show. Its about a bunch of kids that get stranded and are attempting to survive until help arrives. The major difference is that it is set in space. Which is awesome because space is cool. The plot is pretty interesting though some people might criticize it for not having enough explanation of the reasons behind the kids being stranded, but this show is mostly character based. It maintains a fairly realistic(for anime) vibe and probably isn't for those that prefer more lighthearted shows.
The art isn't anything special and the designs all look like they're from the 90s. This isn't all that surprising because the series was first released in 1999. The backgrounds are pretty cool and the rest of the art has aged pretty well even after 15 years. The animation isn't so horrible it ruins the show but it isn't something you would be fascinated by. The art might turn some people off before they even start watching the show.
The sound used in this show is pretty good. The op song has aged well there is this techno rap style where they repeat Ryvius a couple times at the interval halfway through an episode that helps the viewer to distance themselves from the drama that is actually going on in the show. Some people might say that its out of place but if it had been something operatic or super dramatic it would have ruined the tone by making it seem too melodramatic, which was not the point of the show and would have lumped this show in with everything else of its genre. The sound suits the show spot on. I watched the dub and the voice actors definitely managed to voice the emotions of their characters really well. It may come across as a little exaggerated at times but nothing that should make you think that you could do better.
The characters are what make this show great. There are too many to go over any main characters so I won't but most characters change as the show goes on. A character you liked or hated at one point will probably have your opinion of them flip flop at some point. Every character has believable motives for what they do. Viewer insert Kouji Aiba isn't your standard protagonist. He is whiny but he also never ends up powering up to become the big hero, instead watching as the power players make their moves on the chessboard. The only exception I have to these rules is the crazy bitch. You'll probably figure out who that is if you watch long enough.
I really enjoyed this show and would recommend it to fans of stuff like "Lord of the Flies" and "Game of Thrones" mixed with science fiction. Infinite Ryvius uses a greater than average amount of subtlety and implies things younger viewers probably wouldn't catch that you would need to pay attention to understand. It also has its own made up diction that helps to immerse to immerse the viewer the show even if they don't understand what the characters are saying all the time. Infinite Ryvius is targeted towards a certain type of watcher but for those specific viewers the show is above average.