@S_C You should make your image 9:1 (or 20:1 if you want a really tiny button 
) then make the height of the image 1:1
No expert, but tried a bit
I normally use width = 1000px for images as it should do great on a new iphone I believe. If you want to enlarge the image then I go for heigher resolution. Quite a few of my images are stored in cloudinary and then I would often use q_auto setting - meaning going for automatic quality.
Hope it helps