Here’s my approach to comps:
I am happy to work with Ph.D. students doing comps fields in modern U.S. history, U.S. foreign relations, U.S. empire, U.S.-Latin American Relations, U.S./Latin American/European comparative, comparative race and ethnicity, immigration, environment, food, cultural studies, and probably some other topics.
It is great if you have taken a class with me before doing a comps field, but it is not required. If you think you want to do a comps field with me, by all means let’s talk.
I do not provide you with a list. In fact, I believe that building the list is one of the most important pieces of the comps prep process.
I generally ask students to start by making a bibliography of books that you’ve already read in your proposed field and books you really want to read. Think about how to group the books into smaller subsections, each focused around a few key questions and themes. I will give you feedback on books I think you might consider adding or deleting. We will work on developing your subsections, themes, and questions as you prepare for the exam. The questions I ask you on the actual exam will almost always be related in some way to the questions you yourself have posed in the process of building the bibliography.
Look here for my advice about tools for building bibliographies of secondary sources.