Although web-pages turn to various styling techniques, such as big captions, headings, bold text, italics, underlining, etc., in essay documents styling and formatting is irrelevant. The only sections that require formatting or styling are headings (including the title, author, course, etc.), bibliography, and quotes. Other parts of your essay must not include any formatting or styling techniques, regardless of your intuitive need to include them.
Emphasize by content, not formatting or styling
Whenever you feel a certain word, phrase, or sentence requires emphasis, do not make it bold, underlined, or italicized at once. First, think about how you can make an emphasis through the content, not the form. Construct your essay in such a way that this important phrase (or word) reads important, but not looks important. An effective technique to apply when dealing with such styling dilemmas is to imagine that your essay would be viewed in a plain text editor, without any formatting. Would it still make sense? Would it confuse the readers?
In other words, write your paper in such a way, that the contents — words, phrases, and sentences — let the readers know what is important or requires specific emphasis, and do not turn to formatting and styling to achieve this emphasis. Only apply formatting in structural elements (title page, credits, and headings inside the paper), bibliography pages, and in quotes in the body of your paper.