1.91:1 — which is 1440×754 pixels if you want it sharp, and 1080×566 at the very least.
Free, and it exports at 1440×754 without asking.
Landscape. What a shared link shows, and what Facebook prefers.
Use it for Facebook link posts, Open Graph previews and Twitter cards.
Instagram re-encodes every image you upload — no tool can prevent that, and anyone promising otherwise is promising something they do not control. What you can control is what it re-encodes from.
1080px wide is the floor: below it, the upload gets scaled up before it gets compressed, and the text edges go soft. 1440px gives the compressor more to work with, which is why it is the default here. Either way the export is rendered from your original photo at full size, never by enlarging a preview.
Instagram locks the aspect ratio across a carousel: whatever the first slide is, the rest are cropped to match. Picking the shape once at the start — rather than discovering it on slide seven — is the whole reason it is a property of the carousel here and not of a slide. Up to 20 slides, all 1.91:1.