I'm considering using quotations (a sentence to a paragraph) from various pieces of literature at the beginning of each chapter of my novel. The quotations connect thematically to the events of the chapter. However, I'm concerned that this might make a publisher less likely to take my work-- either because it's atypical or because there might be copyright issues. Is a publisher likely to consider dealing with the need to get permission for quotes? If I only use works in the public domain, are there still potential issues? Thanks!
Check your contract (if you already have one). In some cases, responsibility for securing permissions rests with the author. If so, the publisher will not be concerned so long as you deliver the evidence that you have all the approvals.
If you believe that the extracts from other works are essential to your novel (and it was once a fairly common practice) but your publisher is wary of extra work, you could offer to take on the role of obtaining all the relevant releases to remove that potential "barrier".
If you're just using short quotes, like a sentence or two, I think this would clearly fall into "fair use" and not require any permission. If you're quoting more than a paragraph, and your purpose is just to connect your work to some bigger theme, you're probably quoting too much and should cut it down. I take it that you are not trying to create an anthology of classic literature, but to write your own book and connect it to classic literature. If that's the case, then you shouldn't have any problem. I suppose if your quotes are long, a publisher might worry that you are "on the edge" between fair use and a copyright infringement. At that point you could either cut down the length of the quote or get permission. Getting permission might cost money.