Mordred and Andromeda are the two best for newbies by far, in my opinion. Mordred's skills are just so damn strong (puts every affliction on the game on a boss, plus a skill that reduces affliction resistance lol) since afflictions are overpowered and the most important thing to have for killing bosses.
Andromeda is just stupid good because if you can keep your team alive, they can win any fight no matter how tough eventually.
Arthur is a close second to them both, though, since the defense buffs are really strong against certain bosses that have oneshot potential against your team.
If you want Siegfried (to steal MVPs with) or D'art (to farm more items with) I'd suggest unlocking them second - unless you have a godly starting pool of kamis and not just an SR or two like me, you're gonna need a strong heroic soul to carry you through your initial fights.
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Generally speaking though I don't suggest ANY damage soul to start with. You only need three things for the most difficult fights in the game - healing, afflictions, and buffs. Andro brings healing, Mordred brings afflictions, and IMO Arthur is the best for buffs/defense.
The damage from Sieg is uniquely bad because it only works on bosses that rage and then stun, so he's actually trash for running missions. That's also why Solomon is considered terrible - he offers nothing but mediocre damage and usually thats what you need the least to win fights.