Find a meditation teacher and spend some time doing that. Practice > theory.

I'm going to have to disagree. I thought you were talking about philosophy when you mentioned "notions of personal identity and continuity, and whether this is an illusion."

Yes, there are various Buddhist writings about it.

No, I'm not sure that any of them make much sense without actually doing the meditation. There are certain things which are stupidly obvious and okay from a meditative point of view — like "the self is an illusion" — that are either obviously false or incredibly scary from the kind of point of view you're expressing.

I am not an expert in Buddhist practice, though,, and not qualified to provide much advice. I would note that serious current Buddhist writers such as Daniel Ingram make it very clear that people should deal with big psychological and emotional problems before engaging in heavy meditation.