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#11
You aren't going to find something that lets you map to as a drive (automatically at boot) and be shared over the internet. The best you can hope for is a VPN connection that the user has to kick off, follow by the user running a script to connect the drives.
If it is for simple file sharing, you could just look into a WHS 2011 box and have them use the web console. That's your cheapest and easiest setup.
To accomplish all of your goals, the computers would have to be on the same network.