Different types of periodicals serve different purposes. If you need scientific research (which includes the methods, results, and conclusions), you should consider scholarly journals. If the information is cultural you could try popular magazines such as People Magazine or Sports Illustrated for Kids. If your research is specific to a particular industry, you can consult professional journals. How can you tell if the periodical you're reading is considered scholarly, popular or trade? Click the pictoral-links to find out.
One of the best and easiest ways to find additional books or articles on your topic is to use the bibliography or works cited in a scholarly journal to expand the number of sources for your assignment.