Read chapter three.
Good to have a bit of friction between the crew and it makes particular sense between the the tactical and the armory officer. It's something for these guys to work through and clearly the captain is happy to keep her hands mostly off that for now.
Still trying to figure out the time frame for this. The armory officer makes me think this may be set during the early Starfleet days, i.e. Enterprise.
As for what of my work to read, it's really just a matter of what you're in the mood for. If you're looking for novel-length fiction, start with Tempus Fugit
. If you want something shorter, check out the Lower Deck Tales
. These are not chronological and as they hardly feature any of the main characters, you can just jump in and read whichever you like. Or, if you are really ambitious, you could read the entire series in chronological