From what I know, the "Homunculus" is the name given to the Demonologist class on the League side? I could be mistaken (as I play on Empire, I'm not familiar with the archetype names on the League side by heart).
If that's the case (and I think it is, since it's indeed a class that was released in recent years), then the Demonologist class is basically melee (mostly) or close to medium range (it does have some casts I believe, like AoE ground-based attacks). They can be good at tanking in PvE, good at DPS in PvE, and also in PvP as well. It's not as straightforward as the Warrior though. You can transform into a "Demon" form when playing that class and when you do that you have different skills to use (from what I remember).
For the Demonologist class (or, Homunculus, regardless of the archetype name) I would recommend you check on YouTube for guides, because it's not that easy to explain briefly here. But mostly, it's a close to medium range class (mostly melee range).
For Casters, Mages are now very good (they got buffs in a recent patch). But Scouts are also good. You could consider Psionicists as Casters too, they're very good but they are difficult to master (currently they are excellent at CC especially in PvP, however I'm not quite sure if Psionicists are good or if they would be recommended in PvE). I'd recommend going Mage or Scout first. The Priest class is also Caster (most of it anyway) and they're still pretty good (and not difficult to learn, however they're probably situational; Priests in PvE can be both healers and dps depending on the build they choose, however I would not really recommend Priest for dps in the current game environment with other classes being buffed now; there's better choices like Mages at this point).
For Melee, it's pretty straightforward, you have Warrior and Paladin, good pick in both cases (Paladins got buffs in a recent patch as well, they were rarely played but they're now returning in force).
You don't have to choose classes based on my particular recommendations, but I would say:
1) Mage (for Caster)
2) Warrior (for Melee)
Because Paladin does require some micro-management with shields (and rotating between them) during fights (be it PvE or PvP). So I'd say Paladin is probably an 'intermediate' difficulty class, takes some time to get used to. The Warrior is a bit more straightforward by comparison and they're honestly good at both DPS and Tanking without too much of a high skill curve.
For Casters I'd say the Mage and maybe the Priest are the easiest ones (to my knowledge, others may disagree). The Scout is good but requires quick thinking and movement reactions in PvP (you say you prefer PvE but in general being quick on your feet as a Scout is a plus, it's a playstyle for the class really; they're supposed to be nimble and tough to catch, so if you play like a turret and stand in place you should just play Mage instead).
Hope it helps (again, maybe you should wait for more recommendations in this thread other than just me, or I recommend you check on YouTube for gameplay videos of each classes and see how they play nowadays to make up your mind that way).