I get a little giddy talking about rare book hunting, so bear with me — I’ll try to be useful and not fangirl the whole time. For the 'Twilight' series the absolute unicorns are almost always the earliest and most unique pre-publication items: advance reader copies (ARCs) and uncorrected proofs for 'Twilight', 'New Moon', 'Eclipse', and 'Breaking Dawn' fetch attention because they were printed in tiny numbers and usually sent only to reviewers or booksellers. After that, first edition, first printing hardcovers from the original publisher (look for the true first-state dust jacket and the publisher’s number line) are the next tier. Signed first editions — especially those inscribed to someone else or with a provenance — push the price even higher.
Beyond that, the things that make my collector brain light up are small, numbered slipcased or leatherbound runs produced by specialty binders or small presses, limited signed box sets, and rare promotional items (like publisher giveaways, bookstore exclusives, or proof-of-sale advance editions) tied to the movies. Don’t forget the companion pieces like 'The Short Second Life of Bree Tanner' and the later 'Midnight Sun' — their ARCs and signed limiteds also command interest. If you want to chase one, prioritize condition (jacket, spine, no markings) and verified signatures; provenance and a clean number line will often beat an autograph with no documentation.