JSTOR contains full text as well as external links for articles, books, reviews, and pamphlets. To search for only journal articles, check the box next to articles under "Narrow By: Item type" on the main search screen.
The default search is set for the access type of "Read and Download". At your search results, click on Download PDF to access any item full text. To view all content, whether or not you have access, choose "All Content" at the access level.
There is not a way to limit a search in JSTOR to only peer reviewed content. Most of the current content is scholarly, however older materials were not under a peer review process, because it did not exist at the time. More info: