> No souls: you take a definition of "soul" as something supernatural and reject it's existence.
This position is technically called eliminative materialism, that consciousness or the first person experience of reality is an illusion. I find this to be the most absurd idea in the history of ideas, for the simple fact that I have direct experience of consciousness (my own). Or, to quote Descartes: I think, therefore I am.
> Continuous souls
This is a version of Panpsychism. I do not hold this view, but a lot of people that I respect do (for example, Ben Goertzel, the AGi researcher).
> Souls can be an emergent phenomenon out of certain kinds of complexity like consciousness.
This is known as emergentism. It is more or less the mainstream view nowadays with the scientifically literate. I consider it to be pseudoscience, because it uses the term "emergence" to hide a magic step. It is a complicated and technical discussion, but long story short, things emerge from building blocks. Markets emerge from individual transactions. Swarms emerge from certains behaviors of birds, and so on. What are the building blocks of consciousness in this model? I am not saying that they do not exist, but just saying "well it emerges somehow" is the same as believing in the supernatural, but hiding it in scientific language (aka scientsim).
The list above only contains hypothesis based on physicalism (a not super rigorous definition: the belief that matter is the fundamental stuff of reality). Physicalism seems obvious to the current status quo, but if you become more sophisticated with the mind-body problem you will see that it does not really rest on a sold foundation. For example:
https://en.wikipedia.org/wiki/Philosophical_zombie
What the list omits are the idealistic or neo-plationist hypothesis: that consciousness is the fundamental stuff of reality and matter is a second-order phenomenon. I am not defending any sort of supernatural or religious idea, I am simply pointing out that people assume too much out of a lack of philosophical sophistication. Idealism is perfectly compatible with all of modern science, and there is no particular reason to assume physicalism. The absolute belief in physicalism is akin to a modern religious dogma and it does violence to science and extends logical reasoning and empiricism beyond its current limits.