To start, let me make a very strong statement about the state of support for the hardware of this version of Macbook air. The Linux kernel has "Out of the Box" support for all the hardware on this version. So, If you choose any distro which has excellent efi support and the latest bleeding edge Linux kernel you are good to go and try any distro.
I have gone with Arch GNU/Linux and I am loving it. The capability of hand tuning what you want on your laptop or desktop with Arch GNU/Linux is awesome. Coming from Debian GNU/Linux, where there is "flowing" installer where you chose all the options and then finalize the installation, it was different when my arch installer just dropped me to the root prompt and stood there blinking for my command. The exact way how a computing experience should be, You, the user, is the master.
Please go through all the resources I have linked in the previous post. Form your own procedure then You can fine tune it with any gotchas you find in my writeup. Let me be clear here that majority of what I have written here is verbatim copy of the Arch wiki. All the gratitude/thanks/kudos go to the Arch community of devs and users.
Download the most recent archboot ISO
Write the ISO to a USB stick using dd or unetbootin(hugely recomended) or burn it to a CD/DVD.
Prepare hard drive in OSX: (shrink your OSX partition in Disk Utility)
Download refit.dmg(the image file for a mac). Install it on the mac osx
reboot the air and hold the option(alt)key on the keyboard when u hear the start up sound.Boot into osx and reboot two to three times in the same way.
Now plugin the usb stick created and reboot(I would suggest you to get hold of an external dvd r/w, Yes, U can use any USB external dvd r/w. Because I have heard users comment that the dd method is not the best for efi based systems).
Reboot the air and press the option(alt) button at the startup sound.
Wait for a few seconds while refit loads and shows all the bootable files on the air. You will have two images whose logo will be that of a cd disc. One will be named windows and the other will be something like efi.. with the same logo(only the recent arch images have two options)
Select the image with the efi.. on it. Dont do anything on the terminal, wait for 6 seconds, arch will bootup and give you the root prompt and wait for its master's commands.
Be Carful here, Dont select the windows one as suggested in the above guides. There will be some extra steps since grub doesnt play well with efi.
Allow arch to boot.
Now go here https://wiki.archlinux.org/index.php/Beginners%27_Guide/Preparation#Preparation