Jason,
I helped somebody do a very similar thing about a week ago.
The trick is to use the Batch command's ability to construct a file name.
Tell the batch to append, e.g. "-x" without quotes, to the name of each saved file.
The batch runs an Action which does a save as JPEG, resize image, add logo, save as JPEG, then close document.
The output is "<document name>-x.jpg" and "<document name>-x-x.jpeg".
Then use Windows Explorer to rename "*-x-x.jpg" to "*-print.jpg".
Then rename "*-x.jpg" to "*-web.jpg".
See http://forums.adobe.com/thread/1038992?start=32
The name construction that I used there was just an "x" appended to the document name. Use whatever you like. Also juliew subsequently referred to the method as a "double-batch" run, although it is not. One run of the batch will output two JPEGs for each input document.
I hope the disagreements in that thread don't cause too much disruption.
If you want, the Batch command itself can be recorded in another Action which would store the parameters of the batch, then you could run that Action anytime without having to set up the details of the batch each time. It would always output to one specific folder, though.
