Dear Introspective: The Chicago Manual of Style (Chicago) states that internal dialogue and thoughts are often placed within double quotation marks but may also be set in italics or in plain Roman type. Words into Type (WIT) leans toward italics, while acknowledging both quotation marks and Roman type as viable alternatives.
If you already have a publisher, follow their style preference unless you have a valid reason to do otherwise. As opposed to quotation marks, italics offer a clearer delineation between spoken and unspoken discourse. However, long segments of italics are difficult to read. Avoid italics if you use internal dialogue extensively. Both Chicago and WIT leave the choice up to the author but stress the importance of consistency within a single work.
My personal preference is to use Roman type if the context makes it clear that what you’re writing is a character’s thoughts.