Dont let your thinking become so narrow or limited. The best size is the one that works.
WHEN TILING, make the image 1x1 TILES (not pixels) . Sometimes , however the repeating pattern is so small that its good to use a little bigger image. Keep in mind that data is sent in quantum 'packets'. This means , for example, that 768bytes and 1.5K may take the same amount of time to send since they both fit in the same packet; while 1.6k may take twice as long to send since it requires two packets. So in essence you may not even lose any speed but may the image easier for you to manipulate. [numbers are for illustration purposes only]
Tho , for obvious reason this doesnt apply to tiles, it's not just the size of an image that matters; you must also take into consideration the number of http requests. When possible it is better to D/L ONE 60K image than 15 4K images.
hope clear things up for you.