Playable Classes - Overview

For the most part, adventurers in the Realms of Raen'dor use the same base classes as any other D&D 5E setting might; there are no classes that are completely restricted. However, the nature of this setting does affect how frequently certain classes might appear in the world; while you shouldn't feel like you can't play the class you want, you'll get the most out of the world if you're aware how that class fits in/is perceived in Raen'dor! Be sure to communicate with your DM during character creation to make sure you're getting exactly what you want out of your class.
Common Classes
Which classes are commonly seen in the realms? Well, the answer is most of them!

• Barbarian
• Bard
• Druid
• Fighter
• Monk
• Ranger
• Rogue
• Sorcerer
• Warlock
• Wizard

While Fighters, Wizards, Rangers and Rogues are probably the four most common types of adventurers in the world, nobody is going to bat an eye if they run into, say a Bard. Barbarians and Monks don't need to come from wildlands or monasteries, but simply would denote which of the various fighting styles developed and spread across Raen'dor a character might choose. Similarly, Druids, Sorcerers, Bards and Warlocks all become spellcasters through different means, but each of those means is understood/taught in a widespread enough form that the distinctions don't draw much extra attention.
Uncommon Classes
As you likely noticed, all but two of the classes from the official PHB:

• Cleric
• Paladin

This is due to the fact that for centuries, Raen'dor was cut off from any direct influence from the gods of the Material Plane-- and when it finally reunited with the rest of the Plane after the Realignment, most of the gods had either retreated back to the Outer Planes or renounced their divinity entirely. That isn't to say that these two classes don't exist, or even that they cannot draw their Divine magic from a god (some can, and do!), but it does mean that religion and faith are not cornerstones of life in the realms. While the common classes are widespread and can be found just about anywhere, Clerics and Paladins tend to either be tied to a specific order that holds on to these old teachings (such as the Lightkeepers) or from a family/background that has some special tie to a particularly deity. Finally, it must be said that the powers or a Cleric or Paladin-- Divine magic-- can be accessed and manifested without a tie to a deity or divine order (see "Magical Theory and Classification" if this sounds like something you'd like to explore further).
Rare Classes The final two classes are very rare in this setting; if you are interested in playing one of these, it is suggested that you check with your DM before settling on one:

• Artificer
• Blood Hunter

While the rest of the Material Plane was developing technologically, Raen'dor was constantly influenced by Fey magic and old evils from the Shadowfell; this led to many incredible advancements in magical theory, but not so many in the way of technology or artifice. That isn't to say there has never been or never will be an Artificer in Raen'dor (especially when considering that Raen'dor is now reunited with the wider Material Plane), but it does mean that most Artificers would be self-taught-- and their works would likely not be very well understood by most. If you really want to play an Artificer in this setting, consider that your character might be an outsider-- your practice might be looked down on by wizards or other folk, and you've likely been on your own when it comes to learning and mastering your abilities.
Blood Hunters are rare for a different reason: Hemocraft (or blood magic) is outlawed in Raen'dor alongside necromancy, meaning that the base techniques used by all Blood Hunters are also outlawed. This class does exist, of course, and is probably more common overall than Artificer, but the fact that they cannot openly practice their class features makes them scarce. If you really want to play a Blood Hunter, know that it must be kept secret from all but those you trust the most; your kind isn't accepted openly at Nightcrest Academy or the Adventurer's Guild, so if you have a mentor they are likely just as careful about who they open up to as you. 

A Note on Subclasses: With dark magics (necromancy and hemocraft) banned across the realms, keep in mind that certain subclasses might be perceived negatively even if your base class is common/widely accepted. School of Necromancy Wizards, Fiend or Undead Warlocks, Shadow Sorcerers, and Phantom Rogues are all examples of this; if your subclass seems like its going to be exploring what would classify as dark magic, check in with your DM to figure out how you want to justify or explore that! Similarly, the uncommon nature of Divine magic goes beyond the base classes of Cleric and Paladin-- Celestial Warlocks, Divine Soul Sorcerers, and so on might want to consider what led to their connection with this otherwise rare magic.