In 1704 the Boston News-Letter became America’s first continuously published newspaper. According to Archiving America, it mostly covered British politics, ship schedules, sermons, fires and accidents. It was originally published and printed by bookseller John Campbell and appeared weekly on a single page.
Campbell handed the paper over to printer Bartholomew Green in 1722. Under his watch, the paper reduced its coverage of British events and started covering more domestic affairs. A decade later, John Draper inherited the paper and increased its size to four pages, adding news from surrounding colonies.
Take a look at Archiving America where you can see what an early issue of the paper looked like.
Speaking of rare newspapers, look up for a peek inside the rare newspaper archive.