In Preparation For The Job Market - On Day 1 of the PhD
Actually the most important thing for you to focus on right now is getting a good research experience and a good relationship with an advisor. Get started on that. Learn to go deep into some subfield of your overall field. Gain expertise in that. 

Along the way, if you want to be an academic, a bit of teaching experience will help, but will be more valuable for some positions than others. But without the "gain expertise" part it won't matter much. 

And I caution against trying to choose a field strategically based on what is going on this month. You will graduate, in several years, into a completely different job situation and it is impossible to predict how it will go long in advance. As you get closer to graduation, in four years or so in the US, you can start to broaden your skill set depending on the perceived needs at that time. 

But some things are valuable in any case. Learning to do research. Learning to write. Learning to collaborate. Building a circle of potential collaborators.

But most of the details you suggest are just distractions at this time. Day 1 is the day you look seriously for the best advisor willing to work with you.