The best resolution for a computer's wallpaper is one that matches the screen's native resolution. If a wallpaper in native size isn't available, the next best option is choosing one at a higher resolution.
Compared to the size of disk drives, even the largest wallpapers are small. Computers are able to show high-resolution at a lower resolution with only a minimal sacrifice in quality. Using a wallpaper at a resolution that's lower than the screen's native resolution can produce visual artifacts and jagged lines.
It's also important to choose the right aspect ratio. Using a 4:3-formatted image on a 16:9 monitor causes the image to appear stretched, while using a 16:9 image on a 4:3 monitor compresses the image horizontally.