This is not an easy question to answer. The question “Best way to learn Linux” will be answered differently by each person you ask. However, no matter what their answer is the only similarity in each answer will be persistence.
Here is my attempt:
Best way to learn GNU/Linux is by using it
Like with anything else in life the best way to gain skills is by practice. No matter what your final goal in terms of GNU/Linux mastery is, it is important to switch from proprietary software and start using GNU/Linux. There is no preference which GNU/Linux distribution you should choose to use, the only thing which is important is that you get persistent and use it as a main operating system for your activities. As a result, this will seamlessly provide you with an endless learning curve and new skills on daily basis almost effortlessly.
Although you have mentioned that you already have some familiarity with GNU/Linux I would still recommend read through LPI Linux Essentials. LPI Linux Essentials is a beginner Linux certification which will give you a solid, no shortcuts guidance to GNU/Linux background as well as the basic ideology behind GNU/Linux. I’m not recommending that you necessarily need to get certified, all what I recommend is to pick up some LPI Linux Essentials book and use it as guidance through your first steps.
Need for focus
Over the years the term GNU/Linux means different things to different people. Combining this with a vast amount of FLOSS projects being launched daily, one needs to draw a line and decide on focus. This is very important! You already have a focus which is great and is going to help you to achieve your goal. In your case you wish to focus on web server administration so why not start by launching a free tier amazon instance to run your personal blog about GNU/Linux exploration.
Connect with FLOSS project
Once you gain some confidence within your desired focus, it may be a good time to think about joining some FLOSS project to further sharpen your skills. There are myriad of FLOSS project waiting for people to contribute and in return they learn new skills.
Using online resources
To further develop your GNU/Linux skills it is recommended to join various GNU/Linux and specific to your focus related forums, IRC chats etc. Not to only
to seek an answer but also provide help to other GNU/Linux community members. Furthermore, see if you can join your local Linux User Group and mailing list.
Warning: My personal advise is to stay away from Facebook or other mass social media. It is a brain, time and privacy killer
Keep up and stay focused.
Hope this helps.