Puppy seems ideal if all one's doing is copying files - its resource requirements are magnificently low.

I'm out of touch with Puppy - Scyla, just wondering whether you're trying to run a 32-bit version on a 64-bit netbook.

Ubuntu's not really my favourite distro, but if you're comfortable with it, then I'd have thought it would work.

If you've not actually downloaded it yet - you might consider something with better driver support. Mint is less fanatical than Ubuntu vis a vis non-free drivers and I find it pleasanter to use (subjective, of course.)

PCLinuxOS is slowly luring me away from Mint - runs beautifully in a live session and I think it's quicker than Ubuntu.

One of the problems with Linux is the sheer volume of choice. Whichever you decide on, make sure you download a 64-bit version if your computer is 64-bit, a desktop rather than server version if that option arises (not really sure that matters; just never tried a server), and if you're used to the GNOME desktop with Ubuntu up until the latest, you might consider the GNOME version of whatever you choose.

Other than that, I find tossing a coin works pretty effectively in deciding just what to download.