In Dante Aligheri's "Inferno", Ring One was also named "Limbo", and it housed those whom he called the "Virtuous Pagans". It was a place dedicated to those who lived "good" lives, but didn't have Jesus in their hearts (Aligheri was a devout Catholic). These "virtuous pagans" weren't necessarily being punished, but were forced to exist without the presence, or love, of god.
Personally, I felt that Ring One was redundant. There's already a place called "purgatory" (which is basically the same idea), and on top of that, pagans and heretics were cast into Ring Six. So I decided to make Ring One the ring of "judgement". However, Minos, doesn't actually make an appearance till Dante and Virgil make their way into the Second Ring. However, upon further inspection, and after studying a map of the Inferno Aligheri included with the text, Minos actually does reside in the First Ring.
Minos' job is to render judgement on the damned and deciding which Ring they're cursed to occupy. This decision is based on whatever sin you've committed to earn you a place down in the Inferno.