Looking at the specifications, you shouldn't have any problems: they so often come from graphics cards and you have Intel graphics, which is fine. Various distros have been installed on eeeBooks with no serious problems. Linux will be better than Windows in one particular respect: you only have a small HD and Linux takes up much less space.
I would suggest that you go to the BIOS and disable secure boot; I'd also switch from UEFI to legacy BIOS, if possible, but that's not important. You'll be installing from USB stick and I gather that it's best on these computers to get that plugged in before resetting the BIOS to use it.
If you are one of those who dislikes Windows 8 because of its non-traditional GUI, then avoid Ubuntu -- that's the same only more so. A good beginners distro is Linux Mint. Like most, you can run it from the USB stick to make sure that you like it before installing. Have a look at the guide: