A textured background would have to be about 10px x 10px - large enough
for the texture, small enough to have a small file size.
A picture background is much more difficult:
How big is the page?
Does the page fill the browser portal whatever size the browser window
is opened at?
If the page is a fixed size, then that is the size for the background
image, with a colour set for the bits the image does not cover.
If the page size can vary, then either the image must be set to not
tile, or it must be designed so that it can tile either vertically or
horizontally, or both, without looking bad.
The smallest browser window I design for is 800px x 600px. There is no
real limit to the maximum size - my monitor set up will display 2560 x
1024 - other displays are bigger.