I realize most of this has already been said, but just to make it really, really clear...
1) UNR is official, from Canonical
2) IIRC, eeeUbuntu is what Easy-Peasy used to be called, before the devs got a letter from Canonical's lawyers. :P I don't know if they've tweaked it further since the beginning, but as far as I know, it was originally intended to be a more out-of-the-box solution for UNR, before an official UNR image was released. (Thus saving you from setting up the netbook-specific stuff yourself)
3) Mint is based on Ubuntu, and currently does not have a netbook-specific release. However, that's not to say that it couldn't necessarily run on a netbook decently - I haven't tried to see what the performance is like.
4) Kubuntu 9.10 "Karmic Koala" (the release that's coming out this week) will include the KDE Netbook Remix. It is still quite new, but I've been told that the KDE and Ubuntu folks worked to make sure it was ready and working well for this release. It is technically classified as a technology preview, but it is apparently quite usable -- and it looks amazing! Because Kubuntu is just a different spin of Ubuntu, it is entirely possible to install this alongside UNR, given sufficient disk space, however, if you're new to Linux, that might not be the easiest way. I'll try to find a recent demo video of this, and post it later.

Hope that helps.