Is it better to format character thoughts with quote marks or italics? I say neither. No special formatting is necessary to signify character thinking. You just need some solid narration.
Advice and thoughts on narrating to best effect.
Once the author becomes visible, the enchantment of the story dissolves. The author is the creator of a story, but the author should never be a part of the story. The author is the man behind the curtain. Reveal the man behind the curtain and the Wizard of Oz narrative dies. What sorts of things reveal the author? Here are 12.
Information conveys states of mind, states of existence, but not states of affairs (unless you’re dramatizing the past via a flashback, but that’s not conveying the present-time story state of affairs). But if your information (facts, past, interiority, context) is not relevant to the story’s state of affairs, your reader is going to tune it out—or worse, come to distrust your narration.
External refers to what’s happening outside of characters’ minds. It’s the stuff that an observer could see. You could film it pretty easily. Internal refers to what’s going on inside a character’s head: feelings and thoughts. Prose storytelling regularly informs us of characters’ interiority in ways that, say, a screenplay cannot.