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There are several things that you need to consider when choosing your Instagram profile picture. The first of these is that since Instagram profile photos displayed inside a circle (the icon inside which you see your profile picture on a small scale), the elements of focus in your picture should be centered. If they are not centered in the picture, they might be cropped out when displayed in the circle.
Another important point is the size for Instagram photos. Instagram profile photos can be minimum 110 x 110 pixels, and they are stored at 320 x 320 pixels. In the light of this information, keep in mind that you should upload an image appropriate for these dimensions. The best size should be chosen considering these dimensions.
Instagram photo size on your feed: