The automating is the hard part. This doesn't meet all your requirements as some of the software is not free, but I thought it still worth mentioning.
I download a lot of .RARs from Usenet, and before Unison 2 came out (which has automatic Un-RARing of files after download - and is not free) I had to roll my own solution similar to what you're looking for.
Basically I used a combination of Hazel (not free) and UnRarX (free) to do the job. I downloaded all of my RARs to a folder that Hazel watched. When they were fully downloaded (I told Hazel not to do anything until the files were 30min to an hour old) Hazel would open the .PAR2 or .RAR file in UnRarX and then move the unpacked file to a different folder. Once moved, Hazel would then clean the download folder.
It's definitely not a one click solution, but I made a few different workflows to handle different types of files (music, video, etc.) and get them unpacked and sorted where I wanted.
To go totally free you could write some AppleScript and set it as a folder action to do a similar job to Hazel.