Why was Christianity able spread so quickly throughout the Roman Empire and how did Roman and Christian values combine?

The older religions did not provide for an afterlife - some cults did, but were isolated in inaccessible areas, and only the rich could afford to go there and pay the joining fees. So various cults grew up which were prepared to travel to the customer - Mithras, Isis, Christianity etc etc, and they established centres throughout the empire.
Constantine decided that he needed a religion to bolster his imperial power and reach. He followed Mithraism, and had an imperial cult of The Invincible Sun (Sol Invictus), but these did not have central bodies with which he could connect politically. So he selected Christianity whose bishops gave him the control mechanism he sought. He combined Christianity with Sol Invictus and it eventually became the official religion, physically destroying the Mithraists and merging Isis into Mary the mother of Jesus. The images of Jesus and the saints had the Sun behind their head and bodies, much later reduced to a halo to avoid the embarrassment of the link with the sun cult.