Hi Sam, You can use the same version of the document, just place the print image in one branch and the web version in another. (Branches may be LyX's single most awesome, never heard-of feature.)
When you want to compile for print, then activate that branch. When you want to compile for web, activate the other. Then you aren't having to maintain two copies of your document. Generally, I prefer jpeg for photographs. If your using Photoshop or GIMP, you can specify the amount of compression you want applied to the picture. PNG would also work, but it's my opinion that it doesn't preserve color quite as well. Cheers, Rob