My EeePC 701 was the 4GB version, so I managed to hobble along without any compression, but the screen was an issue. I used vnc to control Anaconda from another computer. (http://docs.fedoraproject.org/install-guide/f12/en-US/html/sn-remoteaccess-installation.html)

A Kickstart file is probably your best/safest bet here, though I’m not sure whether you can request compression using this file. I’ve also heard of ways to use yum from a running system (ie. LiveCD/LiveUSB) to install a full system. It gets a little hairy here though, since you need a separate ext4 /boot partition.
I guess you could partition a small /boot partition as ext4 and the rest as btrfs, then (where /dev/sda is your SSD):

# mount -t btrfs -o compress /dev/sda2 /mnt/newroot
# mkdir /mnt/newroot/boot
# mount -t extfs /dev/sda1 /mnt/newroot/boot
# grub-install /dev/sda –root-directory=/mnt/newroot
# yum groupinstall “GNOME Desktop Environment” –installroot=/mnt/newroot –enablerepo=fedora –enablerepo=updates

I’m mostly going from memory here, so feel free to do a little Googling. :-)