I run LinuxMint 7 Gnome on my Acer Aspire One (ZG5) with 160 GB hard disk w/ the 8.9" screen.
works great -sound, video, wireless, etcetera.
Currently connected to a 17" LCD monitor, a USB keyboard, a USB mouse and a wider than telephone internet connection. Wireless worked fine before, but only using the wired connection at present.
Used "xrandr -s 1440x900 -r 60" in a terminal to set the external monitor, but it's easier with the gui app, grandr.
The 17" screen looks kind of weird while booting up but then adjusts itsself to the desired resolution.
I would take a pendrive with a LiveUSB version of LinuxMint 7 gnome to the store and ask them to let you convince yourself that it works as expected. Hopefully they are knowledgeable enough to understand.
I have read that up to the 10" AA1 has same or similar specs to the 8.9" version. The newest one has a different chip and would probably need testing/checking to be sure. I expect that it will work but have never seen one.
sidux tracking testing works OK on this setup, as does AntiX; however, AntiX requires more fiddling around than either of the others, and Mint is the best so far for me on this particular setup. Now some 3 months in use. I only use ppa to get the OpenOffice 3.1.1 version, all the rest of sources list is mostly stock.