When you're ready to shape your notes into a draft, think about different structures for your paper. For example, you might arrange your paragraphs in chronological order, or move from the specific to the general, or from your weakest argument to your strongest.
Use the readings from your class assignments to help you shape the tone of your paper. If the assigned articles use the first person ("I" statements), then usually you can do that, too. If the papers in the field use passive voice, as in many of the sciences, then that's how your paper should sound.
Extensive block quotations are most appropriate when the specific word choice and phrasing of the quoted author is important - for example, when you're analyzing a piece of literature, a political speech, or an interview response. If you're instead trying to convey the content of an argument, then aparaphrase will usually fit better into your paper.