There are Linux distributions in the world with their own purpose. Some distros are built as a modern, beautiful Linux desktop --which needs better hardware requirements. The others distributions, in the contrary, built for speed.
If you have an older computer with older hardwares, or if you just need a fast operating system to complete your jobs, you have to look for these 4 top fastest / most lightweight Linux distributions, but still easy to use as a productive, daily operating system.
1. Bodhi Linux
Bodhi Linux is a community based linux distribution based on Ubuntu. It uses a new desktop environment called Moksha (which is actually a fork of Enlightenment desktop environment). It is extremely, super fast Linux distribution that will make your computer fly like a jet. If you are a speed hunter, this distro is perfect for you.2. Lubuntu
Lubuntu is an official Ubuntu flavor distro. It uses the mature LXDE desktop. It's simple as old cars, but fast as Ferrari. Also, its blueish artwork is very comforting to our eyes. I use this distro for years, as my primary operating system.
3. Ubuntu MATE
Ubuntu MATE is the youngest family member of Ubuntu. It is officially recognized as the member of Ubuntu flavor in Ubuntu MATE 15.04 vivid vervet. Ubuntu MATE uses MATE desktop, a briliant fork of legendary GNOME 2 desktop environment. You would not regret use this distro as your primary OS.
Xubuntu is another Ubuntu family that uses XFCE desktop environment. It is considered fast as a distribution, but sometimes considered slower than the other distro, like Lubuntu. Personally I like this distro because of its Whisker menu that looks like Windows 7 menu. Compared to Ubuntu, and or other GNOME based distributions, Xubuntu is faster. It will run great in moderate hardwares, like low end Intel processors with 2 GB of RAM.