Prior to the late fourth century, the major religion of Rome was what we now call paganism. This was based largely on Etruscan and Greek gods, adapted to the Roman situation. the gods of other conquered peoples were sometimes adopted.
Christianity had made slow but steady progress until the advent of emperor Constantine in the early fourth century, after which it grew rapidly, to become the state religion in the last decade of the fourth century.
Mithraism was a contender, alongside Christianity, as the potential challenger to paganism, but faded in the third century and lost out entirely in the fourth century. Mithras was a sun god, as also was Apollo, the sun god of traditional paganism. A later sun god, associated with Mithras, was
Sol Invictus.
Other minor religions of the early centuries CE were the mystery religions, and syncretisms of Greco-Roman gods with Egyptian gods.
In the rural areas outside Rome, as well as in Rome itself especially in its ealier years, animism was a key religious element.
Pagan, although I hate that word. they worshipped the many gods who rerpresented the powers that the Romans experienced in their daily lives - the powers of nature - the powers of the mind - the powers of the body, no personal, single god.
Constantine merely removed any penalties against Christians - official policy was neutral towards any recognsed religion as a result of his edict of 313 CE; it effectively allowed Christians to aspire to high office. What he did do (although a Mithraic initiate himself - his conversion to Christianity is suspect) was to broker a merger of the imperial cult of Sol Invictus with the mystery cult of Christianity (that's where the halos came from - the Sun). He chose Christianity over other mystery cults because Christianity had a controlling hierarchy of bishops, which made it easy to manage as a unifying factor in the empire.
The Romans saw their state religion as a compact between the state and the gods. They gave the gods due respect and deference and expected the gods to look after the state. They also had special-to-family gods who looked after the family and hearth, plus some earlier earthy forces like the Lares. Then there were the mystery cults which promised an afterlife - Mithraism, Isis, Christianity, etc etc which became popular, often in parallel to the official and family ones. However Christianity separated itself from both its parent Judaism and the state religion, and when it gained control either destroyed the other cults or absorbed them (eg Isis and her titles were absorbed into the Mary sub-cult of Christianity).
Pagan was simply a term for country dwellers - not part of the citified folk. It was used for those who were not citizens and participants in the state religion. Christianity has since used Pagan as a derogatory label against those who did not adopt its faith, just as Muslims quite easily label those not of their faith 'infidels'.