Ok now I'm curious, which class would contain the most of Heroic Spirit Theo?
This is something I've actually put a fair amount of consideration into since I got into fate. Short answer? Ruler.
On a longer note, Theo would have four classes he could be summoned as, most likely, going from least to most fitting they would be:
-Assassin: An Embodiment of theodores suppressed ruthlessness and the aspect of himself that wanted to, and did, follow in Taylor's footsteps. Pretty much devoid of the rest of who Theo was, or at least suppressing it. Theo would often prepare, learn, and study before an attack, and would just as often attack from afar as he would up close. Thus making him a candidate for the Assassin class.
-Berserker: the aspect of Theodore revolving around and defining his righteous anger and hatred against both Jack and the empire. A cold fury that simmered beneath the surface, only emerging in rare bouts. Though it wasn't known to most, we see it in his interludes and his fight against Jack. Qualifying him, to some extent, for Berserker.
-Lancer: Theodores more chivalrous and Heroic side. Defining hid want to help, to remember the fallen and save who he can. Though Theodore doesn't use a spear, not all lancers do, such as romulus, Elizabeth Barthony, and enkidu, use methods other than spears despite being lancers. The same goes for Theo: with his fists acting as his "spear".
-Ruler: the closest thing to the true Theodore. A Theodore that died in middle age. The type of person we see in ward, where he has moved past what has happened, and accepted his regrets, helping others, such as rain, move on. He is no longer bound by regrets, thus no longer covets the grail. As a keeper of law in life, he thus will act as one again in death. A Theodore who has finished his journey.
Those are my thoughts on Theodores classes. As for why Caster isn't among them, generally we see casters as either actual spell casters, or as story tellers(like shakespeare) neither of which are really something Theodore was. I won't say he can't qualify for it, but the problem is, other than territory creation, Theodore doesn't have an other skills or noble phantasms that would make him qualify for Caster. It's just not a class he's well suited to.