recently found my passion in Linux systems

Seriously, find another hobby. It's ok to enjoy your job, but take some advice from someone who's been there, if your job and your hobby are the same you will get burned out.

I have been thinking of this idea to host a web server

As a Linux admin I'd expect you to be able to do this. "Install nginx/apache" is one of the basic tests I do in hands-on interviews. You should be proficient at building and tearing down servers.

document everything as updates to the webpage

I skill I do NOT expect Linux admins to have is web design skills. Showing me your web design skills has nothing to do with your Linux Admin skills. They are really two different disciplines with little to no overlap in skillset. (Hosting a website is different than building a website)

While a "repository of knowledge" that you can refer back to is a great idea, that doesn't really seem like what you're talking about here...

To build a "knowledge repo" build yourself a Wiki. There's plenty out there (heck, you can even build your own "Wikipedia").

I will have sections that highlight my implementation of tools such as Docker, Ansible etc as well as a means to show what I know.

Ok, let's say you want to hire a Carpenter. Would you want to see how he implements a hammer? Or do you care about the result of the work with a hammer? It depends on the job certainly, but generally speaking, no one cares how you did what you did with docker, what's important is the end result.

Do you think that this is a good idea?

A web page is no substitute for a Cover Letter/Resume. Do both, or at least have a Cover Letter and Resume.

I have this idea of using Docker to contain my web server app,

is your website stateless? Then probably a good use-case for docker.

database

Is your database stateless (hint, no it's not), then probably NOT a good use case for docker. Docker is a fine tool, but it's more like a dual-claw hammer. Sure, you COULD use it to pound in nails or screws, but there's probably a better tool...

maybe use Ansible

YES! I'm a big Chef fan, but learn your CM tools today. (some more info on CM here)

Learning Config Management tools/concepts will put you ahead of a lot of the market out there. (I still interview people who think they can do a better job than an automated procedure... they are consistently wrong)

as demand for space on the website grows

Unless you're allowing uploads, your website isn't going to "grow" any significant amount.

But again, the "install web server", "clone website code", "configure webserver" steps are all things that can and should be automated.

Nagios/Zabbix Squid

YES! Monitoring is a huge weakpoint in most organizations I've worked. Getting good at monitoring (install, configure, manage, not just "can you look at a monitoring tool") will set you apart (at least from the candidates I've been interviewing lately...)

So, to summarize. Find a hobby that's not "IT". You will benefit yourself more by building a useful tool over just a "website" (e.g.: wiki vs static blog). A website is not a replacement for a Resume/Cover Letter though can certainly be used to augment either. And finally, go get your hands dirty! build VMs on your home computer, sign up for a free account at AWS or GCE. Or go get a cheap VM at a provider like Digital Ocean.