I'm going to actually going to say "it depends". You say its for offsite file backup. But it really depends on how much data, what kind of data, and what kind of technology you're leveraging.
Backing up Deduped and Compressed Virtual Machines for instance is much more CPU intensive than say, FTP'ing your photos.
I had a Crashplan system doing Crashplan -> Crashplan backups that were deduped and compressed with about 8TB of files, and it would choke unless the Java Virtual machine was given about 6GB of RAM and 4 CPU cores.
Knowing a bit more about what you're using to backup would give better answers I'd say. But in general, for home users just doing generic file backups, any old thing off the shelf (even a little old Atom machine) would likely be fine.