How DPI becomes pixels, and how to choose it
PDF measures pages in points, where 72 points is one inch. An A4 page is 595 × 842 points, which is 8.27 × 11.69 inches; Letter is 612 × 792 points, or 8.5 × 11 inches. Multiply the inch dimensions by your chosen DPI and you have the output pixel dimensions: A4 at 150 DPI is about 1240 × 1754 pixels, and at 300 DPI about 2480 × 3508.
Choose by how the image will be used, not by what sounds high. Something displayed in a web page at 800 pixels wide gains nothing from a 2480-pixel render except download weight. Something that will be printed at full size needs 220 DPI or more, because printing a 150 DPI raster at page size is visibly soft.
A useful check: if you will be zooming in to read something, you need more DPI than if you will be glancing at the whole page. The cost is quadratic — doubling DPI quadruples the pixel count and roughly the file size — so the step from 150 to 300 is a bigger commitment than it looks.