The preeminent name in Khazar studies has long been Peter Golden. He is, for example, the single author with the most works listed on the Wikipedia Khazar page. There's also a nice bibliography under his own Wikipedia page as well. His work does range from highly accessible to obscurely esoteric (he's a master of little-known languages), and I'm sure prices on these volumes vary significantly as well.

Unfortunately, I expect that many of these publications will be too expensive for an individual to buy, but Golden has kindly made several of his foundational works available for free download at academia.edu. (You may need to register a free account to download.) Beyond Golden himself, I'd probably trust any of his collaborators in the volume of articles titled The World of the Khazars, although you'll have to look these authors up one-by-one to see if they've written anything book-length that you're interested in.

More broadly, it's worth looking at how the Khazars are discussed by authors in tangential fields. Off the cuff, I'd probably take a glance through the works of Jonathan Shepard and Wladyslaw Duczko on the neighboring Viking Rus, as well Roman Kovalev and Thomas Noonan who have studied the movement of Arabic silver coins northward from Central Asia toward Scandinavia.