Hi Kittie,
I was wondering what you meant by applying to Classical Linguistics programs? As far as I know (and I've researched this a bit, since I myself partially geared my grad school applications towards programs with a linguistic leaning), there are only Classics programs, or Linguistics programs, although Cornell specifically has a phd specialization in Classical linguistics (and for that I think you would need a bit more experience on the linguistics side of things, since you actually apply to the specialization). However, there are a few schools with scholars who work on classical linguistics, and you can always talk about those profs in your SOP (SUNY Buffalo, UCLA, Princeton, and the ma program at Georgia all come to mind). If I were you, i would do some reading about classical linguistics, and then in your SOP I would talk about a couple of professors that you think you would like to work with at the school, not just classical linguistics people, and I would also say something like "In addition, I have recently found myself interested in classical linguistics, and in particular I am eager to explore [whatever/something sort of specific that maybe the professor has written on]. Working with Professor x would give me the opportunity to further develop my interests in this field, and that is one of the main reasons why your department would be a good fit for me" - except in a much more exciting and articulate way.
As far as reading goes, I like Fortson's Introduction to Indo-European Linguistics, although it can be a bit too technical especially if you don't have a linguistics background (which I don't), for introductory reading books on historical linguistics are good, I like Anthony Arlotto's, and there are also the Vox Latina and Vox Graeca.
Hope this helps!
PS. Don't feel bad about not knowing a huge amount about Classical Linguistics, the field unfortunately is sort of unfashionable, and so it's very hard to be exposed to it from the Classics side of things. As far as I know, very few undergraduate programs offer even a class on the subject, and none offer a program of study at that level.