To which language family does Chinese belong, or what's in a name?

There are at least five competing theories about the linguistic prehistory of Chinese. Two of them, Tibeto-Burman and Sino-Tibetan, originated in the beginning of the 19th century. Sino-Caucasian and Sino-Austronesian are products of the second half of the 20th century, and East Asian is an intriguing model presented in 2001. These terms designate distinct models of language relationship with divergent implications for the peopling of East Asia. What are the substantive differences between the models? How do the paradigms differently inform the direction of linguistic investigation and differently shape the formulation of research topics? What empirical evidence can compel us to decide between the theories? Which of the theories is the default hypothesis, and why? How can terminology be used in a judicious manner to avoid unwittingly presupposing the veracity of improbable or, at best, unsupported propositions?