Yes you'll need some Fat32 space...
I'd back up over the network....But you can play around with both methods and see which works best for you.
SyncBack is a flexible, and quite powerful backup and synchronization program that allows to to maintain backup copies of your files and folder, or to synchronize them, so that both locations always have a complete copy (e.g Laptop/PC). It offers different types of actions that let you choose how older and newer files are processed, which files should be excluded (by mask) and more. It offers standard file comparison based on the date and size, as well as optional MD5 checksum, which will detect even the slightest modifications to files.
SyncBack also supports scheduled projects, FTP and zip compression of backups, as well as network login, simulation runs and more.
http://www.snapfiles.com/reviews/SyncBack/SyncBack.html