I'd imagine the best way to 'tackle' it would be to have a few different protagonists - I think the setting lends itself to that sort of approach.
Taking Star Trek's original 'wagon train to the stars' mantra and running with it a little - I'm visioning lots of small ships like runabouts making the voyage out as groups for the sake of protection (presumably having a few adventures along the way) and upon reaching their destination being amazed by how 'rough and ready' life there is. The field would be awash with like-minded people, tough preying on the weak, precious equipment and supplies being bartered and stolen since resources are so finite and so on.
Each of these ships would have a tale to tell.
One story might follow two young men arriving in what is essentially an oversized shuttlecraft (possibly someone with a larger ship is bringing these low-warp shuttles out from the Federation for a fee) with virtually nothing to their name other than their little ship.
Another story might follow a larger, more well-funded mining ship and its crew.
Another could deal with the man who is in de facto
'charge of one of the asteroid settlements, keeping order and dealing with the people coming and going - perhaps one of these hundreds of people is murdered while at the settlement and he has to track down the perpetrator out amongst the asteroids - perhaps he rounds up a posse!