Jack Campbell's The Lost Fleet (Starts with Dauntless) is possibly something you could look at. It's largely battles in space, but there's a lot of focus on the internal politics of the fleet, and there are sections where the marine force do become a focus. They're very trashy, pulpy sci-fi with a lot of similarity across the books (And I mean a lot!), but they're by no means bad.
David Weber's Honor Harrington series may also of be of interest. Again, ship focused but with a lot of ground and political action. A warning, though. It's quite technical and Weber seems to lecture the reader about the technology more often than not, so it might be a bit much for you - I know I struggled a lot with the books I've read.
In a little twist, it might also be worth your time to look into books from Black Library. They publish the Warhammer 40,000 books and a lot of those are more infantry based, especially the Imperial Guard novels. There's two big Imperial Guard series which may work for you. The first is Gaunt's Ghosts, which I believe is a fairly standard but immensely popular series revolving around a group of soliders. The second is Ciaphas Cain, and that's a more light-hearted series with a number of funny moments. There is some 40k lexicon thrown around quite often, but for the most part you can get a good idea of what's being said.