Film and film holders are more readily available and less expensive than 5x7 or 8x10. The experience gained in building and using the smaller size may be valuable when designing a larger camera. Larger film (or paper) sizes do have a modest advantage in image quality.

This is because the image blur is proportional to the pinhole diameter. The ideal diameter (for maximum sharpness) increases in proportion to the square root of the focal length. Therefore, if the focal length is doubled, the blur is only 1.4x as large. For the same reason, wide angle pinhole cameras can have better central image sharpness than longer focal lengths. However, edge sharpness and illumination suffer in wide angle pinhole photography.

I prefer film over paper in the camera. It is easier to capture quality images on film. Paper has limited color response and demands more careful exposure. Exposure errors in film are easier to correct in printing. When printing, images on film can be interpreted in more ways than those on paper. The higher cost of film is small in comparison to the investment of time and energy in making and using pinhole cameras. With care, film can be processed in the same developer as paper. I often do this to increase contrast. It may also increase grain, which shouldn't be important in an image that has little detail and might never be enlarged.

For well over a hundred years there has been much (and sometimes heated) discussions on the optimum pinhole diameter. For maximum sharpness it is more critical than many claim. I prefer Pinhole Designer with a user constant of about 1.4 for optimum on-axis sharpness with film. With this criteria, the diameter for a 170mm focal length could be about .43mm mm for film and a little smaller for paper. The diameter might be increases a bit to sacrifice a little central sharpness for better corner sharpness with wide angle pinholes. Few lenses make an image as unsharp as a pinhole photograph. Sharpness is not the main goal in pinhole photography. More important is how pleasing or effective a slightly unsharp image can be.