Story:
RnHS is one of the light novels I love the most. It's characters are well made and have a "thick" credible personality, the plot is well made, without falling to the easy traps of the "MC transported/summoned/reincarnated to a medieval fantasy world" genre. The country the MC arrives at is medieval India-ish with magic, but neither is that magic so OP that the MC forgets everything from our world nor is the MC some omniscient man knowing how to improve farming, medicine, cooking, how to make stealth bombers from scratch... In fact the magic is not all that powerful and the MC has the layman knowledge in most topics, furthermore he has more or less decided to affect his new world as little as possible (no technological breakthrough). His aim is mostly to live with his wife while not hindering her work (she is a queen in a male dominated society, after all). So what is there in this story?
To quote the comment of Elaborate on Novel Update,
There's not that much action, and what action there is, the MC is generally not involved with. He IS learning magic, but in a very realistic fashion, it turns out to require around three years of studying to use it, so that's not the focus of the story either - we just see him studying from time to time.
So what's left? Married-couple romance with the Queen, doing the taxes of an entire kingdom with a computer spreadsheet, carefully NOT getting too involved in court politics, trying to invent soap before the supply runs out, negotiating trade routes, teaching the maids to play video games... In short, situations you basically never read about!
The manga itself (currently read until ch3):
The drawings are of good quality
The manga adaptation took some liberties from the LN version. While it is understandable that some explanations are shortened and put in a totally different way than in the LN, other modifications are simply unforgivable:
The story begins with some "premonitory dream" that simply breaks the universe' consistency before it's even been established. If the author wanted to put that scene in the first chapter (to get the readers interest?), why not make a flashback? After all, the novel did it, even if it was not from that same specific moment.
The MC is an intelligent modern Japanese man, but for some reason, the manga makes him dumber and more perverted than necessary. At least that is the feeling I got from the 3 chapters available at the moment.
Conclusion: Wait and see
If the original story is not too altered by the adaptation, this will be a great read for anyone who enjoy a slice of life story with a bit of politics.
If not, well... this could turn out to be some shitty moe-ized adaptation.
I really hope the quality of the adaptation will improve to make justice to the original works!