You don't actually have to crop your photos to get them to show up pretty big on IG.
If your photo is in a 4x5 ratio (horizontal:vertical), it *will* show up at the maximum possible size on IG on a phone or iPad. What I do is add white bars to the sides of my images to get them to a 4x5 ratio.
I generally size small JPEGs at 2,000 pixels in the long dimension (as that pretty much fills my iPad's 2048 pixel high screen)--IG won't show them *that* big, but I can't be bothered to resize them again for IG. So if I've shot something 2x3 or 3x4 (my ancient digital back on my Hasselblad), to get them into a 4x5 ratio, I just set Photoshop to make the canvas size 1600 pixels by 2000 pixels, so it adds white space to the sides of vertical photos. (Horizontally oriented photos are a bit more problematic, and IG doesn't play as nice with them.)
If you don't have Photoshop, there are loads of other apps that will add the white space to the sides of your images to get them into 4x5 ratio, many of them free.
If you'd care to see my own Insta, and see how I've maximised the size the photos will show up there, I'm @presquevuphoto on the 'Gram. Cheers!