So is a variant rule so it's up to the DM from the beginning. There are no references in XGtE or VGM about it, at least not one that I remember from when I read them or one I could find in a quick search. From the beginning that there are no hidden rules, we can assume that if the spell list was meant to be limited to some kindI would say yes, as for Mindflayers (who have Wizard spells), Driders (who have cleric spells) and others.
Volo talks about Kobolds, which are draconic creatures linked to dragons, and their spell casters are Sorcerers (p.64), if that helps you at all.
My personal guide on how I ran dragons in the past is simply Choose the one that makes the most sense for your dragon., as you described in your fourth bullet.
Remembering the casting spell divisions is something that can help you decide which one makes the most sense.
- Arcane or divine? The Spellcasting chapter describes how magic works by affecting The tissue. There are two types of magic: Arcane or Divine.one.
- Spontaneous or prepared? Spontaneous spell casters simply know spells, such as Warlocks, Bards and Warlocks, while prepared spell casters have access to many (usually all, except Sorcerers), but can only prepare (through Praying, Studying or something more) a limited number, such as Clerics, druids and magicians.
So, which ones fit your dragons better?
one PHB, p. 206:
The spells of magicians, sorcerers, sorcerers and bards are commonly called arcane magic. These spells are based on an understanding, learned or intuitive, of the operation of the Fabric. The caster plucks directly into the threads of the fabric to create the desired effect. Eldritch knights and arcane cheats also use arcane magic. The spells of clerics, druids, paladins and rangers are called divine magic. The access of these spellcasters to the Weaving is mediated by divine power: the gods, the divine forces of nature or the sacred weight of a paladin's oath.
While there are some spontaneous pitchers (Sorcerer, Warlock, Bard), those described as born with that magic that runs through their veins are the Sorcerers (under unexplained Powers, for example):
People with magical power boiling in your veins Soon discover that the power does not like to remain silent. "
In addition, the sorcerers have the Draconic Bloodline origin, placing them again as the closest to the dragons, one of their possible magical sources. is the same as the dragons.
Finally, notice how the text describes the casting of the dragon's spells.
Dragons are innate magical creatures that can master a few
spells as they get older, using this variant.
A young or older dragon can innately cast an amount of
spells equal to their Charisma modifier. Each spell can be cast.
once a day, without the need for material components, and the
the level of the spell can not exceed one third of the dragon
Challenge rating (rounded down). The dragon's bonus for
hit with spell attacks equals your skill bonus + your
Charisma bonus The spell of the dragon, except DC, is equal to 8 + su.
Domain Bonus + Your Charisma modifier.
From this text, the resemblance to the Sorcerer is quite large: they use the same modifier of Charisma (as opposed to Wisdom or Intelligence) and it is likely that their spellcasting uses their own understanding of the Weaving, not the intervention of some god like Tiamat or Bahamut. For that reason, I usually use as default that dragons are spell castors similar to sorcerers, and a few Dragons are exceptions to that, for example. A dragon who spent his life studying magic fits better as a magician, as you said, and he would change his spell ability to Intelligence as well. However, this is completely within the scope of home management or even home-made.