1. "guess" - original meaning - you don't know the answer to a question and you say something which you are not sure is right. e.g. If I had to guess, I would say that the sun is 100 million light years away (but really I have no idea).
2. "suppose" - deduce speculatively from the evidence e.g. I suppose that you're late again for dinner because you've been drinking with your friends in the bar. Am I right?
3. "guess" - informal, casual meaning - "think", "believe" "suppose". It's very similar to "suppose". e.g. I guess that you're late again for dinner because you've been drinking with your friends in the bar. Am I right?
"suppose" suggests more serious thought but really it is interchangeable with "guess"