Some interesting points here. I'll give you my theories about it:
1. Chakotay had commanding experience. According to Jeri Taylor's book "Pathways" he was Lieutenant Commander and second in command on the ship Gettysburg before leaving Starfleet. He was also Janeway's Number One on Voyager. So it was logical with him in charge when the Captain was on some away mission. Maybe it had been more logical to send him on away missions more than he was but Janeway would gladly take part in those missions herself and Chakotay wasn't like Riker who didn't like the idea of the Captain taking such risks.
2. Paris had showed early on that he was a reliable force on away missions and since he obviously liked to stick his head in dangerous situations, he might also be a logical choice.
3. B'Elanna had such skills as an Engineer which even Carey couldn't match despise his Starfleet education, therefore she was given the job. I do find this a sympathetic move from Janeway, to give a real talent with such skills the job. There might also have been some other aspects here. B'Elanna was regarded as a troublemaker. A troublemaker with talent but still a troublemaker. By giving her responsibility, she found it easier to adapt to the Starfleet life. Besides that, it was also a signal to the Maquis on the ship that anyone could contribute and get an important job.
4. Kim had some skills when it came to computers and engineering besides his job at ops. It might also have been a way to make "young Ensign Kim" feel important and be apart of his development as a Starfleet officer.