What does the (hypothetical) soul take with it?

[FatAndFaithless]

Buddhism was 'logical and scientific' and 'incredible for its day' in what way?

I'd recommend the book "What The Buddha Taught" by Walpola Sri Rahula. In it it talks about what the Buddha, as a person, taught and there is nothing metaphysical about it. He comes across as an expert in psychology and the ideas make a lot of sense. If I were to follow any 'religion' that would be it but at that point in time it was not a religion, just the teachings of a wise man who never claimed to be anything other than that - he did not believe in any god nor claim to speak for any god.

I'm familiar with the stripped down meditative and contemplation-focused version of Buddhism (Four Noble Truths, Eight-Fold Path and all that), but I wouldn't call that anything 'scientific', nor especially astounding for its time. Additionally, if there's any hint of samsara or karma or anything like that, then any veneer of 'scientific' really goes out the window.