#1 believe: Something you know for sure based on the information you have.
#2 bet: Something you "assume", you do not know for sure, you do not base your assumption on fact but most likely on previous events. (e.g. "I bet Jim will be 30 minutes late tonight, he always does").
#3 think: Pretty much the same as believe, but a little weaker.
#4 guess: It is something you assume to be, but you have no real information or previous experience to support it.
#5 suppose: Same as "guess" and "assume" ("guess" comes from a Germanic root, "assume" and "suppose" come from a Latin roots)
#6 assume: Already explained.