Bernal spheres and other O'Neill cylinders are complicated, maintenance-high and fragile beasts. Someone started to make micro-black-holes and put them in asteroids, in order to have 1 to 10+km rock spheres with ~1g of surface gravity, and started terraforming those.
The micro-black-hole is in a state of equilibrium: too small an event horizon to efficiently feed, the pressure from its Hawking radiation keeps matter from falling into it. Let's assume the entire thing is stable on a geological scale. (How would this work is the subject for another question elsewhere, let's assume here that it does.)
What would the atmosphere of such a planetoid look like? The goal is to make it as adapted to unmodified human life as possible. So the right amount of nitrogen and oxygen, water vapour, ability to retain some hydrosphere, shielding from radiation, stable temperature... Distance to the Sun, rotation period, exact radius and surface gravity that can be tweaked as necessary, and a molten core can rotate at a different speed if it helps generating a magnetic field. What would the ideal (or as best as possible) atmosphere look like, and how stable would it be over a long time period?
This question was originally inspired by the book Revenger by Alistair Reynolds, where most of the Solar system seems to have been converted to those, though most don't seem to have much of an atmosphere.