I'd just read that Augustus was not pointing it out too clearly that the Republic was dead and that Rome had become a monarchy, that's why he used always the title princeps meaning the first among equals. He still refered to the Senate which was still influential though not as much as before. Instead of two leaders, the consuls, which were elected for one year, he was now the sole head of the Senate for his lifetime. Therefore I would say that Princeps Senatus was his most important title.
Was there ever a Roman Emperor who was considered already during his lifetime as God? Many of them, even Augustus were deified after their death. The Romans always looked down on the oriental kingdoms who declared their kings as gods like the Egyptian Pharaohs etc.