It depends what you mean by set criteria. There is no ruling paradigm in biblical studies, or history, which would provide you set criteria for evaluating historical sources.
In history/the field of historiography, the general skills of the traditional historian were largely influenced by Leopold Ranke, who pioneered source criticism and archival work. Valuing documents which were not the official memoirs of great figures (the stock and trade of much history), but instead minute books, occasional documents, common receipts, notes, etc. Most practising historians that actually do the work of generating new historical narratives of a particular subject, do so on the basis of primary documents, archival documents, incidental and non-curated documents, etc. Those are probably close to the standard criteria for traditional practising historians. But their criteria likely vary case to case, given their subject matter, the evidentiary remains they're working with, etc.
Philosophers of history (some of them, yes, are practising historians), and many biblical scholars focus on theory and method more than many practising historians in other fields who, unlike biblical scholars, have loads and loads of new materials to work with at any given time.
The criteria used by Biblical scholars varies from discipline to discipline, and usually between those who differ in methodological presuppositions. There is a tacit collusion between traditional evangelical approaches to biblical history, and traditional critical approaches, all of which see some sort of positivist, rationalist, if not empiricist nature in the historical enterprise. The idea here would be to reconstruct original unknown sources (even if hypothetical) (Q, or the autographs of the New Testament manuscripts), or to state what "actually happened" regarding the historical events. A representation of traditional / conservative scholarship (I don't mean this pejoratively, these are good scholars) would be the recent book Jesus, Skepticism, and the Problem of History. More moderate scholarship which shares in many presuppositions, but tends to have a more critical notion of the idea of doing traditional history, would be found in a work like Jesus, Criteria, and the Demise of Authenticity.
In history in general, a lot of good resources exist. Your best reference work for the contemporary philosophy of history is, in my opinion, hands down: the Blackwell Companion to the Philosophy of History and Historiography.
Mainstream critical biblical scholarship tends to tire of traditional historical questions. In my opinion, some of this tiredness is justified (e.g., good linguistic and literary questions have been wrongly overlooked, and some historians have not appreciated the unavoidably linguistic nature of the discipline), some of it, in my personal opinion, is less so (e.g. some see the idea of history as outmoded, hegemonic, patriarchal, etc. and would prefer a host of critical theories to take its place, others see it is skeptical and would prefer theological readings). Regarding the latter, it isn't that there is nothing to learn from such studies, they vary in value from work to work, and person to person. Class Struggle in the New Testament is an example of a work which takes a technically modernist approach to historiography (Marxist historiography), but of course it is understood to be imbued with other modern, critical notions. Such works might not be of interest to you, but if you're looking for a consensus among biblical scholars as to how the Bible should be understood historically, you won't find it. You'll find various camps, who adhere to various methods and tools on the basis of widely differing presuppositions regarding the nature of language, history, epistemology, metaphysics, and the like.