I've written that I put Ubuntu 8.04 Hardy Heron on my 8G EEE PC 701, but I didn't tell the story of how I did it. So I thought I'd take a moment to explain all the steps I took.
First was the USB image for installation. Using a dedicated 1G usb key, I prepared it as a live image cd using the iso2usb script found here. This created a usb key from which I could boot just as if it were a live CD.
Second was the installation. I chose filesystem ext3 with no swap. I had issues with ext2 losing data, and removed the swap to decrease the read/write access on the drive. I would recommend a 70%/30% split between the root partition and the home partition.
Third, I used a second usb key to save a single folder with three items, one was the tarball downloaded for the madwifi source code, the ubuntutweak shell script and a simple text file for my steps to follow. The text file is the first paragraph from the Ubuntu EEE wiki page that describes the wifi fix.
Upon first reboot of the freshly installed system, the wifi won't work (ethernet port will). With the source and instructions on a second key, I copy them local on the non-networked EEE for permenent usage. I run the wifi fix first which requires a reboot before taking effect. I then proceed to get online since the ubuntutweak script will need internet access to download some files, packages and source. This batch of fixes will also require a reboot.
At this moment you would have a working EEE PC (700 models 4G/8G) working with all the hardware working. There are is still compiz - contrain y setting to fix and to remark the cdrom line of /etc/fstab. More problematic is that there have been kernel updates since the iso was released. Kernel updates break any/all compiled drivers. So the previously copied folder of wifi/ubuntutweak will be used any time there is a kernel update. This won't be an issue if you leave that folder on the system in your home directory.
I've used this through 2 kernel updates on my Ubuntu 8.04 system since instlaling on my EEE 701. I've also just walked through all of this on a brand new 700 model (purchased by a new user) which validates the process as working.
I have spliced this install/fix process together from the Wifi fix page and the general fix pages from Tux Family.org and give them credit for all of their hard work. Obviously once full support is built into Ubutnu (fingers crossed for 8.10) then this process will be a non issue. I hope my hints make your EEE PC transistion just a little bit easier. With the recent development of the Ubuntu Netbook Remix interface, my hopes are high.