I use Elements too and do any sharpening as the last step before saving at the final use pixel size.
I generally resize down to 1200x800pixels, either by resizing via the image tab or by cropping to it when reframing and/or straightening horizons then use the Unsharp Mask in the Enhance drop-down menu, using a standard (for me) threshold of 0 levels and a radius of 1 pixel then using the slider to get as much sharpening as necessary to improve the shot while trying to use as little as possible. Finally I save at as high a quality as possible to be under any file size restriction there might be, meaning that (hopefully!) any host will not need to do anything to the file to degrade it further.
Any adjustments I do to a file are made to a copy rather than the original file and I always try to do the whole edit in one sitting since it doesn't take many open/save cycles to degrade JPEGs even at level 8.