Colour management - HUGE file sizes

This is getting to be a real conundrum, and I appreciate any suggestions:

When creating JPGs or GIFs for the internet, obviously my greatest concern is not how they'll look on my own monitor, but rather how they will look on thousands of other monitors.  My question is what are the best general colour management settings for either CorelDraw or PhotoPaint when exporting to JPGs or GIFs -- without creating files of enormous proportions?