If your image has few colors, with large areas of the same pixel (like screen captures), use PNG. It uses RLE compression: if there are 50 consecutive pixels of white color, for example, it will just encode "50x white".
If your image has no pattern, and 24 millions colors (like a photo), use JPEG.
To disable alpha-blending in SFML, do this:
window.draw(sprite, sf::BlendNone);