Help with valuing a rare (or so I'm told) book set?

AbeBooks in the UK has first editions of Burton's Arabian Nights in 8,000 to 10,000 pound range; current exchange rate is about .62 pounds to one dollar. So, yes, if you have a real first edition in good shape, it is worth some money. I wouldn't fiddle around with eBay or Amazon for something serious. Find a reliable antiquarian bookseller, for example through the Antiquarian Bookseller's Assoc. of America or a state or regional association. Your librarian (or an English professor if there is a largish university nearby) might be able to suggest someone reliable.