It depends on whether you're using iOS or Android. If you have Lightroom mobile, Dropbox, or an Eyefi card, it's pretty easy to get them on your phone.

If you go the card route, editing with Snapseed or Lightroom mobile, and VSCO will be enough.

If you insist on working on the desktop since that's where the sausage is usually made, just export it so it's no bigger than 8mb or so so you don't kill your phone.

Instagram no longer forces you image to be a square, but it will appear cropped in you gallery. If you wanna get around that, you can use a photo framing app like SquareSize.

Other than that, use the small size of insta to your advantage. Because of the resolution, you can post those ones that you like that aren't tack sharp enough to print or post full res; no one will be able to tell. This also means you can use it as a space to be a little more relaxed and experimental. It doesn't have to mirror your portfolio. Create material specifically for Instagram, which is probably gonna be less boring.