Hi, i've got an EeePC, too. I'm using it with a n-lite shrinked version of XP that uses only 103MB RAM after fresh installation.
Today my EEE has got 1024MB of RAM and I virtualized a lot of Windows and Linux systems using VB just to demonstrate people that it's quite possible.
Now to answer your question, DSL (Damn Small Linux) is really the smallest Linux i've ever seen before, I use it in fullscreen 800*600 using AsTrayPlus on host to adjust the resolution and it works fine.
DSL comes with included firefox, most commonly used apps (e.g. text/spreadsheets, players, etc.) and some games.
Everyone is thinking that I installed a linux on my EEE, but they are very surprised if i'm telling that it's just virtualized. They are asking "how could it be?" and i answer: "look at this, everything's possible".
The same way I virtualized the original Xandros of the EEE in VB, just for fun!
Just for fun, I'd started a Xandros and a DSL VM parallel at XP host, allocated 256MB RAM to each of the quests.
Everything of that suits in the 4 GB SSD of the EEE 701, no need for SDHCs or USB-Devices.
Finally I would like to recommend antiX, a small Linux Live CD using a 180MB ISO but doesn't need to have a virtual harddisk, very fast and secure if you attend to surf fast and secure.
Just read this: