The Monster Manual describes a Variant rule for Innate Spellcasting for dragons in p. 86. The book does not specify a specific class for the spell list, so which spell list do they use?
Possible rulings that I know:
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Book does not specify a list. Pick and choose any spell from any list.
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Sorcerers and warlocks have 'granted-spontaneous' magic, so do dragons. Choose from sorcerer and/or warlock lists.
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Dragons obviously serve/worship Bahamut/Tiamat. Hence: cleric spell list.
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Thematic approach per individual dragon (with examples): One Silver dragon is very paladin-like, so paladin spells for him. This Green dragon is 'very smart' and researches a lot – so wizard-list for her, with many books in & around her lair. Pick one list / stick to it.
Are there any official rules (in books, including VGM or XGtE or Crawford's tweets) clarifying this matter?
Best Answer
Not specified, so the DM chooses it.
Well, it is a variant rule so it is 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 principle of there are no hidden rules, we can assume that if the spell list was intended to be limited to some class, it would say so, just as it does for Mindflayers (which have Wizard spells), Driders (which have Cleric spells) and others.
Volo does talk about Kobolds, which are draconic creatures linked to dragons, and their spellcasters are Sorcerers (p. 64), if that helps you at anything.
My personal guidance on how I ran dragons in the past is simply choose the one that makes more sense for your dragon, as you described in your fourth bullet.
Remembering the spellcasting divisions is something that may help you in deciding which makes more sense.
So, which ones do your dragons fit better?
In particular, Sorcerers are probably the closest to Dragons
While there are a few spontaneous casters (Sorcerer, Warlock, Bard), the ones described as being born with that magic running through their veins are the Sorcerers (under Unexplained Powers, for example):
Additionally, sorcerers have the Draconic Bloodline origin, putting them again as the one closest to dragons - one of their possible magical sources is the same as dragons.
Finally, note how the text describes the dragon spellcasting.
From this text, the resemblance to Sorcerer is quite huge: They use the same Charisma modifier (opposed to Wisdom or Intelligence) and it's likely their spellcasting uses their own understanding of the Weave, not intervention of some god like Tiamat or Bahamut. For that reason, I usually use as default that dragons are sorcerer-like spellcasters, and a few dragons are exceptions to that, e.g. a dragon that spent its life studying magic fits better as a Wizard, as you said, and I would change its spellcasting ability to Intelligence as well. This is completely on the realm of house-ruling or even homebrewing already, though.
1 - PHB, p. 206: