I'm not sure if this is the right place to ask this --- if it isn't, I'll delete it.
The question is prompted by the internet speeds at my address. To download a large file (say, 4GiB or so) several hours or more are needed.
Thus the answer to this question would (maybe/likely) include/be a linux on a board that has a very low power draw and that has a usb port so that storage can be added to it, in addition to Ethernet connection. This would be connected to the (slow) internet connection and left on 24/7. At certain times of the day a script will run which will trigger the system to sync its files with Remotehost. So that's,
ETHERNET --> SOME_TYPE_OF_LINUX_SMALL_SYSTEM -- SCRIPTS -- --> EXTERNAL HARD DRIVE
Software wise I suppose any distribution would do; seemingly a headless system would be best so perhaps Arch linux. The biggest part of the question is then, if you agree with what I presume to be the best way to go about this, what hardware models/company makes such a device?
EDIT: The answer should not be the raspi, but rather an already assembled unit.