Well, then I take it that you'll be using something like BackupNT to perform the backups? It doesn't matter much. There are a lot of ways you can perform backup.
But as for the server itself, it's really only going to be a target for a copy/sync operation. So it can run any OS. I suggested FreeNAS, since it's more lightweight and may perform a little better, besides taking up less space with system and program files that could be used for data.
Why don't you try it and see how it works?
Of course, you could always just use an external hard drive. Again, if you need is a destination for files, it could be almost anything.