Steins;Gate gets quite dark and serious, but it starts out pretty goofy, so if you’re trying to avoid comedy it would leave a pretty bad first impression. I don’t think I would recommend pushing yourself through the earlier parts to get to the later parts either, because you do need a certain attachment to the characters to appreciate the latter.

Vinland Saga, from what you’ve written, seems more up your alley. In a similar vein (bloody serious historical fiction) I also recommend Orb.

Other than that, Pluto and Monster, both thrillers based on manga by Urasawa Naoki, are very straight-laced.