Ariel may have been the only good-aligned mage, but she was there with them on every show, and since the bad guy mages kept on being defeated on every show, you need more of them, works pretty much the same in a standard D&D campaign, also in a standard D&D campaign, you need a balanced party, Thundarr's party consists of two barbarians and a mage. I would make Ariel a sorcerer as per the D&D 3.5 class Sorcerer, but I would allow sorcerers to pick from two spell lists in the player's handbook, either from the sorcerer/wizards spell list or the list of cleric spells.
A sorcerer can cast cleric spells just as if they were sorcerer spells, in that way, a character like Ariel can heal damage, which is a realistic campaign will be needed quite often, because characters will take damage. Their won't be actual clerics that can cast spells, and since their won't be clerics, we won't need gods either!
The magical radiation which caused the civilization ending disaster also gifted some people with the ability to use magic, this is an inborn trait, kind of like a mutation.
I also don't expect magical items to be very common, technological artifacts kind of replace them, such as Thundarr's glowing sword. So lets review the character classes that exist, they are Barbarian, Bard, Druid, Fighter, Monk, Paladin, Ranger, Rogue, and Sorcerer. I put a question mark next to Paladin, they don't seem to fit in. I think one can argue for the other classes. Thundarr is a Barbarian, I think people even in post apocalyptic times will have an appreciation for music, and hence Bards, Bards are like Sorcerers in that their magical abilities are inherited from their parents rather than learned.
Druids worship "Nature", there is no specific god of Nature, but somehow they have a way with nature, can communicate with animals, and some can turn into them, you might call that a mutation. Like Barbarians we also have Fighters, kind of hard to tell one from another, but perhaps fighters are a bit more educated, and have more experience with artifact weapons, the weapon types a fighter can use is expanded, they can shoot laser rifles for example, they are familiar with all things combat, they can pick up a gun and shoot it, barbarians aren't as familiar with those types of weapons.
There are Monks, always were Monks actually, some of them have gained some abilities members of their order didn't have prior to the end of civilization, but they have carried on their traditions and practices nevertheless. The Paladin is a bit iffy. No particular reason why their shouldn't be Paladins, but they seem to be specific to a medieval setting with notions of chivalry and all that, not sure this world has a lot of that, its only been 500 years since the end of civilization. A Ranger fits in better, there is a lot more nature since the end of civilization, more forests too. 500 years is plenty of time for new forests to grow, and their is not as much land under cultivation as their used to be, the unused land grew back into forests as they once were. Rogues exist because their are always people who steal things and who have developed a set of skills to accomplish larceny. And their are sorcerers but no Wizards. Magic is an inborn trait on this world, one is born with it, learns how to use it, but first of all one must be born with it. Magic use is a kind of mutation, one can develop that skill with practice and experience, but one must first be born with the necessary trait.
