There are three types of magic: arcane, divine, and innate.
Arcane creatures: any PHB spell that affects evil creatures affect all arcane creatures (dragons, fey, fiends, giants, gods, undead). This includes dispel evil and good, hallow, and holy aura. Spells that specifically affect only undead still only affect undead arcane creatures.
Conjuring and Summoning: divine magic cannot summon other creatures. Remove all spells with these effects from the Cleric and Paladin spell lists.
Creating Undead: powerful Arcane magic can animate the bodies of anyone, mortal or arcane, who was not properly buried by someone with the Devout Belief feat or who did not have Devout Belief at the time of their death. Fortunately, this magic is used infrequently at best: the secrets of animating mummies seem to be known only to long-undead Kaikuhurans, and nearly all vampires are created by another vampire, not by pagan magic.
Dispelling: arcane and innate spells can never counter or dispel divine spells: there is nothing in Arda that can match the will of the True God. This includes antimagic field, counterspell, and dispel magic.
Healing: all three types of magic can heal or cause injuries. Add cure wounds, heal, healing word, mass cure wounds, mass heal, and mass healing word to the spell lists for all classes.
No Planes: Although both arcane and divine magic come from outside Arda, both are fully expressed within Arda. There is no power within Arda that can transport a creature outside Arda: only the True God's grace allows a soul to leave the Cycle of Arda for whatever waits beyond. Arcane creatures live throughout Arda, on cloud castles, high mountains, forests, and underworlds. Elemental creatures can be found throughout Arda wherever there is a concentration of their element.
Reviving the Dead: It is possible to revive the dead if the dead creature's soul remains part of the Cycle of Arda and the person is willing to return. Any mortal person properly buried by someone with the Devout Belief feat or who had Devout Belief at the time of their death cannot be brought back: their soul has left the Cycle of Arda, either for heaven or nonexistence, depending on who you believe. Innate magic can interrupt the passage of a deceased creature's soul through the Cycle of Arda and prematurely restore them to life in a new body. Arcane magic can break the Cycle of Arda and bring the soul back to its dead body, either as a living creature or as an undead corpse.
True Names: All living things have a soul, and all souls have a True Name. It is different from the creature's common name, or their name in this life. Most creatures that know their True Name keep it a well-guarded secret, because someone who knows magic and knows your True Name has an advantage over you. At the minimum, any time a spellcaster casts a spell using a verbal component that incorporates a target's True Name, the spellcaster has advantage. Some spells have particular effects that are enhanced by knowing the target's True Name: for example, revivify and reincarnate will always bring back the soul of the creature being restored to life if you call them back using their True Name.
The World of Spirits: In addition to the physical world, there is also the World of Spirits. The World of Spirits is invisible and overlaps the physical world: creatures in the World of Spirits can see the physical world, but everything looks gray and ephemeral. The souls of the dead enter the World of Spirits as part of the Cycle of Arda, and usually return to the physical world only when born into a new body. Some souls that cannot or will not to give up their past life can enter the physical world, taking on limited physical existance with an insubstantial and translucent body of mist. Magic can allow the living to see into or travel through the World of Spirits, though usually at some cost. All spells that include ethereal travel or teleportation involve travelling through the World of Spirits.