I have an Acer Aspire One. The specs are 1 GB RAM, 1.6 GHz Intel Atom.
I'm looking for the fastest version of GNU/Linux that is fully functional for this netbook. I do NOT want to run from a USB as my netbook is purely for Linux. So far the only thing I've been able to get to run correctly (with small issues) is Ubuntu 12.04 with Xubuntu interface.
I have a Samsung N150 Plus which have an Intel Atom N455 1.66GHz and 1GB DDR3 (all the specs here) and I'm using Lubuntu since 11.04. I use it sometimes to read PDF, navigate with Chromium, write LibreOffice texts, play Spotify music, ear practice with GNU Solfege and watch videos (offline 720p videos without problems, some 1080p are perfectly decodified).
I tried Unity (Ubuntu 13.04), but is so heavy for this computer if you want to use Spotify and Firefox at the same time, for example. Same with GNOME 3. GNOME 2 also works perfect (by default before using Unity in Ubuntu), but I think that is not an option nowadays. Also, you could try Xubuntu (I use it in my main computer with Ubuntu Studio) and seems similar to Lubuntu using resources (XFCE maybe is a little bit heavier but incomparable to KDE, GNOME or Unity).
So, with my experience with that kind of computers I'll recommend you to use Lubuntu, but you can also try Xubuntu (or Ubuntu Studio if you use that computer for multimedia development) or even Ubuntu (Unity) with classic environment. Install the release version that you want. I always use LTS versions because are more polished than the latest ones, but maybe there are things in the latest release that makes the difference with your hardware.
I have a Netbook, an Asus EeePC with AMD C-60 APU. I'm running Gentoo on it, since source based distributions like Gentoo are definitely the fastest ones. Gentoo might be challenging, because there are many things that can (and will) go wrong with a Gentoo installation. If you are patient (compiling webkit can take a night or so), have fun playing with a Linux system, customizing the kernel config and fine tweaking sytem settings, Gentoo definitely is the distribution for you - like the Gentoo website says: "Gentoo is all about choice". If you just need a system that just works and you don't want to invest much time in, then don't use Gentoo.
In such a case, I strongly recommend Debian Wheezy, which I had installed on the Netbook before I switched to Gentoo. Debian is very similar to Ubuntu (actually, Ubuntu is based on the "unstable" Debian version), but the Debian developers care more about stability than about new software-versions. Therefore, the just released Debian Wheezy has many software versions, that Ubuntu had in 12.04 (and some even older ones). The great thing about Debian is, that if one selects a lightweight desktop (like Xfce) when booting the installation CD (even before the installer is started, directly in the GRUB menu, under advanced options), it comes with even more lightweight software than the light Ubuntu versions. Also, I found that some programs are in the Debian repositories, which are missing under Ubuntu. There are drawbacks of course, the most important being that Debian Wheezy uses an older libc than Ubuntu 12.04, so Ubuntu 12.04 packages will in many cases not install due to missing dependencies. Also some convenience tools of Ubuntu are missing in Debian (instead of PPAs, one has to add the full deb-repository URL, there's no software center,...). In addition, Debian has the non-free repository, which contains for instance the GPU drivers for AMD and nVidia, disabled by default (it's not difficult to enable it, but it might be that after installation the GUI does not start and one has to use the command line for driver installation...).
Fastest is going to be Gentoo with a custom kernel and only the applications you use optimized for your hardware. It takes a long time to learn to install, compile, and optimize gentoo, however, and you are not going to notice a huge difference if you use a binary distro such as Arch Linux, Fedora, Debian, Slackware, or Ubuntu.
You are going to get the most bang for your time by performing a minimal install of Arch, Fedora, Debian, Slackware, Ubuntu, etc and install only the packages you use + a light weight window manager such as Openbox.
If you want a preconfigured distro take a look at Slax, Slitaz, TinyCore, Crunchbang, Zenwalk, and puppy linux.
Here is a list of versions and the recommended specs:
Installation/SystemRequirements
I would suggest a minimal install with the Lubuntu desktop for its lightweight GUI.
Also the Ubuntu Netbook Edition may be worth looking at as it is designed more for your system.
Give Lubuntu a go. I have the same computer model as yours and Lubuntu works great. As an advice I'd recommend to increase the RAM to 2GB, you'll notice the difference of performance.
