Here's a couple:

• run Linux as your primary operating system, on both your desktop and your laptop, if any
• install KVM and virt-manager and build a couple of virtual machines
• build a package for your distro of choice (a .deb or .rpm file); it helps in understanding a lot of things
• build your own kernel

These might not seem directly related to your own personal goals of learning to build web servers, but I assure you, if you understand Linux, you will build all kinds of servers easily.