The best aspect ratio for photos you post to Instagram is 1:1 (square).
Now, some readers are thinking, “duh! of course!” but actually it’s not so obvious anymore now that Instagram allows you to post photos of any aspect ratio.
However, Instagram will truncate the top and bottom of portrait-oriented photos if they are longer than 4:5, and landscape-oriented will not maximize the screen real estate that Instagram makes available.
Furthermore, in thumbnail view, Instagram always crops your photos to a square which may seriously weaken the composition if it was composed for the common 3:2 aspect ratio. Your photos have to look good in thumbnail view if you want click-throughs!
So while I think that 3:2 is the best aspect ratios for photos in general, for Instagram you should go with the square!