Another thing that should be added to your description Al is the resolution. When you go to change the image size you need to first check what the resolution is - it could be as high as 300 pixels/inch for printing, but for use on the web it only needs to be 72 pixels/inch. Set that first, then set the long edge (either Width or Height) to 800 pixels.
On the version of Photoshop Elements that I am using (PSE 9) when you go to save your JPEG file and the JPEG Options window opens, as you slide the quality up and down it will actually indicate the APPROXIMATE size of the file, so you don't need to compress more than necessary - 7 seems to be a rather heavy amount of compression which may make visible degradation of the image. The actual file size does seem to be larger than that indicated, so perhaps it does not calculate including the size of the EXIF data. You can see the actual size of your file when you view all the file details in List mode in Explorer or Finder.
I'm not a big fan of sharing all that EXIF data myself and find that it really makes a difference to the size and quality of the images I can share on this site. So I prefer to either use Save for Web or strip out the metadata in Lightroom. If I think it relevant, I can add the exposure details in the description.
Bear in mind that the more colour and detail in an image, the larger the file size will be and the more likely it is to show the effects of over-compression. A picture such as this rose which is basically just a few shades and shapes hardly needs compressing at all to get under 250Kb
This was saved with the EXIF data using Al's basic method in PSE9, but the compression factor was 10 rather than 7.