Although Eeebuntu is meant for Eee PC netbooks, it runs fine on the Acer Aspire One & Gary Rennie published a great tutorial on how to run it from a SD Card.
According to Gary Rennie "The Aspire One works nicely with many Linux distributions, but there had been hardware issues in particular the Atheros WiFi support". Both the 'Standard' & 'NBR' versions of Eeebuntu have good WiFi support.
Installing Eeebuntu is just like any typical Ubuntu install, but installing it onto a SD Card is a bit adventurous on the Acer Aspire One, the BIOS doesn't see SD media but there are a few tricks so you can boot Eeebuntu from a SD card on the Aspire One.
Look here for the great tutorial on the OSnews.com site.