I checked a few references, and the advice varies a little. 11 pt seems to be roughly average, with the caveat that it depends on what kind of book you're doing and what font you use. (Children's books typically have bigger print, for example. Times New Roman gives a similar feel at 12 to what Adobe Garamond Pro does at 11.)
I've never heard anyone say the page size matters when selecting a type size. Really small mass market paperbacks used to have somewhat smaller print I think, but for most sizes, I wouldn't think that would be desirable. (And those really small ones, with almost no margins, aren't a good model for us to emulate.)
People more familiar than I with design might want to weigh in, but I understand Times New Roman isn't well regarded as a font choice for books. As with size, I just checked a few references, and TNR is mentioned in passing as one commonly used in newspapers. It never seems to be the one recommended in articles that discuss good font choices.