I don’t think, in the standard course of historical research about any given figure or event, I would say one starts out as “skeptical.”  It’s not, in my experience, the historian’s inclination to just systematically doubt all claims to historical fact in ancient sources.  That would render every source “guilty until proven innocent,” in a way, and undermine the credibility of all the sources at one’s disposal.  This is especially precarious for ancient historical figures or events, because usually the evidence we do have is sparse.  Like a historian of ancient and modern India once quipped to me: “trying to reconstruct ancient Indian history with the little archeological and textual evidence we have is like trying to do astronomy by shining a penlight into outer space.”  To render all sources suspect from the get-go is not, as understand it, the historian’s stance.

Instead of being initially “skeptical,” I think the historian, and in particular the ancient historian, is “agnostic.”  There is archeological evidence or lack thereof, there is material culture evidence of other kinds or lack thereof, there is textual evidence or lack thereof.  Competing claims and deductions are made, and then one goes about trying to reconstruct the most probable and consistent account of all the evidence.  What the historian is doing is trying to work their way from a position of not knowing to a position of knowing the most probable course of events.  But arriving at the most probable account is tricky, and it involves a lot of interpretation, conjecture, guesswork and preferring certain methodological approaches to others.  

So I would think that a historian’s attitude toward the canonical Gospels, for instance, would be from the start–“Ok, we have these claims about historical fact here.  How many of these can we verify, not verify or remain unsure about based on everything else we think most probable about the period?”