Both Arthur's passive and personal skills are relevant and useful throughout the entirety of the game. His personal skill scales infinitely and for this reason, he almost HAS to be S. He can perform well in any of his available classes due to it making suboptimal classes have access to damage dealing capabilities while making good classes just scale better.
Aegis - Arthur's worst class, unless he is just buffing someone else with Repulsor Shield, and then he's still really good at it because of his higher passive mana regen.
Geomancer - A solid class for any of the mages early on with the free Light Block, decent distant heal (that can cleanse debuffs), and decent warp mechanic that can damage enemies and self heal Arthur. Really not much to write about but it does do its job well in the early game and has the highest Mastery.
Warlock - This allows Arthur to perform a pseudo/off tank role. Poison Nova is really good - especially in Demonic. Do be careful of giving him the Sanctified Ring early on because while he will take less damage with higher defense, he can't heal if he doesn't do damage; though a high power Focus weapon can help solve this problem a bit.
Scholar - Both an overrated and underrated class. As Arthur boasts the highest passive mana regen (Cassandra has higher potential if not for her class tree), Arthur is one of your best "Mana Batteries". Basically every time a character gets low on mana, you Ancient Writ them giving them a large amount of mana back. This scales and you will eventually give more mana than the skill costs. Not only this, but Phase is a solid movement skill and having the self cast on it makes it almost as versatile for chasing objectives as Reaper - a tier 3 class. Additionally, both Ancient Writ and Phase have debuff cleansers which are pretty helpful in Demonic. Lastly, totes the highest speed growth within this class tree and gives you free Fortitude.
Necromancer - Probably Arthur's best class due to him scaling really well with his personal skill and him wanting to get as much mana back to continue to obliterate everything. While there's nothing wrong with promoting him from a Warlock, I find his access to Phase and Ancient Writ a little more worthwhile than the ability to heal on a poisoned target when Drain Life and other healers exists. Because he will be killing most things with his personal skill, you can abandon attack power and use the Sanctified Ring. Just make sure when you kill things, its within 2 and not 3+ spaces or he won't get mana back.
Cosmician - With Cosmician, Arthur's personal skill is good on turn 1, though you'll probably use Astral Reckoning for the same cost until his personal outperforms it. Additionally, Astral Reckoning makes for a decent dual purpose aoe attack and heal. He makes especially good use of the Mystic, Lava, Cleave Ring. Because you aren't getting 20 mana back for every kill within 2 spaces like with Necromancer, you will want to conserve a little mana use on your skills unless you have a Mana Battery for him, so be mindful of that.
Loremaster - This class's only saving grace is its passive. Luckily, the passive is good and it does stack. with 4 Loremasters, you can take a 100 mana costing skill down to 52. Not quite 50% and definitely not 60% as it would imply, but still pretty good no?
Relic Knight - Not really worth mentioning. He can do it, but why?