I have guessed that a 16:9 format is best but what resolution/pixels is ideal?

For menu background images in DVDA6, I've long used snapshots from Vegas Pro's 4K timeline so the images used in DVDA have been 3,860 x 2,160. But since DVDA rendering will reduce this resolution to HD 2,160 x 1,080, I would think that the best resolution for DVDA menu background images would therefore be 2,160 x 1,080 or above. Like with any image, the lower the resolution, the more noticeable a drop in quality will become apparent - but then that can be a compromise call. Also, an image editor may be able to uprez an image to improve the image.