Right before pressing the render button, selecting the right resolution for our image can be a puzzling decision, as size most directly relates to render time. However, it is not a linear relation. An increase of 200% in the resolution panel actually means four times the pixel number. Depending on the specifics of the scene, this can lead to an increase in render time from two to five times or even more.
Still images intended for print require larger sizes, but having to print a larger poster does not mean a larger render size. Recommended print resolutions vary according to the distance the print will be viewed from. A small print up to A4 size will need the fine print detail of 300 or 600 dpi, a larger poster for display on a wall will do fine with 150 dpi and a large billboard will look ok from across the street or from a car at resolutions like 10, 20, or 72 dpi. A trick to determine the pixel size from final print size and print resolution without making calculations is to use the image size settings from an editing software like Gimp.
Another important setting in the render panel is the AA (anti aliasing factor). This setting has a big impact on render time, but also a great importance to the render’s appearance. The default setting of 8 works good enough for most scenes, 5 will show jagged edges and higher values give smoother looking edges. Some workarounds are used, like rendering with no AA at a larger render size, then blurring and scaling down in post processing. This might be considered but is most likely to take away from the quality of the image.
In BI you might need to use Full Sample AA to override technical problems with alpha transparencies and compositing, but be prepared to deal with a much longer render time.