Recommended image size from this article is:
http://www.esri.com/esri-news/arcwatch/0513/make-a-map-tour-story-map
For each point in your map tour, you will need two image files: one at full size for display to the left of the map and a small thumbnail image for display in the thumbnail strip underneath the map. Images should be in JPEG format.
For full-size images, landscape (lengthwise) orientation is recommended instead of portrait orientation. The recommended image size is 1,000 pixels wide by 750 pixels tall (a 4:3 aspect ratio). This will ensure your images look sharp on a variety of monitor sizes and fill the image area to the left of the map nicely. Images in the common 3:2 aspect ratio also work well, in which case 1,000 pixels wide by 666 pixels tall is recommended. Don't worry if your images don't match these recommendations exactly, because images that are larger or smaller or have a different aspect ratio still work.
The thumbnail images should be in landscape orientation and ideally 200 pixels wide by 133 pixels tall (3:2 aspect ratio).
Dear Tom,
I am new to this, but just curious where your images are hosted. The ones I host on Facebook pop up very fast in a story map. It seems that images under 99 kb allows the user to control compression, according to: http://havecamerawilltravel.com/photographer/facebook-image-quality-issues
So maybe that is the size for which to aim. My pictures hosted on FB show well enough I think.
Which Story Map application are you using? There are several: App List | Story Maps