What type of evidence?
The evidence that led people to their belief of course. It's not up to me to double guess what that might have been.
This is a much better way to phrase your question. Still, the word "belief" makes it less than perfect. When e.g. scientists are led by evidence, is the result a "belief"? The way "I believe" is colloquially used in English makes it often synonymous with "I suppose". Evidence surely leads to stronger conclusions than this.
Okay, to answer the question, the evidence is experiential. Which means it's perception for all practical purposes. Experiential evidence is most convincing for one who has it, but most difficult to convey for outsiders. To someone with unsympathetic attitude it's also futile to try to communicate it, but to give an idea about it, there are recurrent experiences, inexplicable by any materialist or atheist theory, that over time become impossible to deny and require a straightforward acknowledgement in the name of honesty to oneself, if not for any other reason.
Another evidence is logic. In nature, in the mind, and in metaphysics there are no empty spots, no gaps. This is why atomism as an ontological stance never made sense to me. By atomism I mean the belief or theory that everything is made of particles and compounds of particles. It's implicit in primary school physics course. Naturally the question arises, what is between the particles? Atomism doesn't answer this. Moreover, the usual well-known problems with ontological dualism are multiplied with atomism, because there are not just two kinds of particles, but more, and there are numerous particles wandering about randomly.
This ontological problem can be solved with continuum theories, best by means of the concept of spirit. Different from particled matter, spirit leaves no gaps in reality, and this corresponds perfectly to what is experienced in external nature and in the mind. This can be called philosophical or logical evidence for spirit. Physicists are looking for a unified theory, and when they find it, the result will be the concept of spirit.
Besides the concept of spirit, there are the logical distinctions of appearance and reality, accident and essence, particular and universal, object and subject, which all lead to God as a logical conclusion, if the enquiry is intense enough.
So, the strongest evidence is experiential, which combines several aspects of experience. The second kind of evidence is intellectual, logical. There's more evidence, such as testimony and scriptural authority, but these stir up more controversy than solve anything, and they have had no role to play in my own convictions, so I won't say anything about these, unless specifically asked.
On the nature of conversion, I have earlier recommended a good English bildungsroman "Of Human Bondage" by W.S. Maugham. Conversion is a coincidence or accumulation of multiple events (psychological and/or physical) that impel one to a substantial revision of convictions. It works in both directions. Who hasn't gone through it has next to nothing relevant to say on this. A single piece of evidence may not look like much, but several kinds of evidence coinciding or accumulating over time will lead to clarification of convictions, sometimes also to conversion.