You can do this free. Create a maintenance plan to back up the DB, you can define the location you want to send the file, and add a clean up task.
If it's express and you can't use maint plans, use this tool to run the backup job automatically: http://www.codeplex.com/ExpressMaint and use a simple VB script to clean up the folder as a windows scheduled task
Then create a script to FTP the logs home nightly as windows scheduled task.
We do pretty the exact same thing in one of our setups.
If the offsite server is on a constant VPN with the DB Server, you could DFS the backup folder.
EDIT: If you are wanting to this as "extra" full backup along side local bks, you'll need to use a TSQL statement for the backup job in the plan, and throw in the "COPY_ONLY" for the backup, so differentials aren't using that as their reference, but your local fulls as planned.