My recommendation is to use what I use.
Fetch what you need from the "Binary Releases" link on the upper left side of the page at
http://www.imagemagick.org/ unless you want to "roll your own at home," in which case fetch the source code instead.
It's primarily a set of command-line tools. I'd be glad to help you with getting up to speed with the command-line if you're not already acquainted with it. I should think just a few basic skills (understanding command formation in general, really) is all that's necessary for the simple manipulation like we're talking about.
The command I'd used on your image was:
<font class="small">Code:</font><hr /><pre>convert -strip -quality 75 <your_image>.jpg <new_image>.jpg</pre><hr />
With just slightly more command complexity, it's possible to make "webifiable" versions of an entire directory full of the high-quality images you want to archive. If you've got decent command line tools on hand you can process an entire directory
structure (hierarchy) in one fell swoop.
The unix version of the package has almost all the manipulation capabilities available via the graphical image viewer component. This may include the version for the Mac as well, since that's unix inside. I'm not sure about that though. Ironically, the last time I looked at any rate, the Windows version has a viewer which can do little more than display the image!