A mix of all three most likely. Demon Parent might’ve been a Spirit Bound demon, perhaps bordering on a Cosmic Bound, but then became a Flesh Bound. Demons aren’t trapped inside these classifications, but it takes a significant amount of energy to change from one “class” to another. Being half human half demon, the MC is naturally predisposed towards the Flesh Bound class, and while it will be possible to expand their abilities into the other classes, it may take even more effort for the MC to fully transform from one class to another.
For example, as a Flesh Bound you can subvert the natural laws and temporarily have - not grow, because that’s following those laws - an extra pair of limbs to make a quick escape from your pursuers. Using the energy you’ve devoured, you can exercise and gain mastery in skills that the Spirit Bound class uses i.e. vacuum ghosts to your location, latch and leech off of potential prey, and craft your own demonic artifacts.
Bonus points, because you’re half demon, you have the potential to obtain longevity and “eternal youth” via two routes, and if you’re not afraid to cross a few moral boundaries 
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If you’re more experienced in your Flesh Bound powers, you could subvert apoptosis and autophagy (programmed cellular death) and necrosis (cell death due to external factors). If you’re more experienced in your Spirit Bound powers, you could just body surf to the next healthy host.
I have no idea how that would translate into stats though. 