I completely agree with this advice! Find a task that you repeat all the time and automate it. A pretty good place to start is just python, git, and bash. When I start a new job it's actually what I do to get my bearings. I keep a written journal of tasks, I make a notes README, and document repetition. I make bash scripts for shortcuts and to prove things, then I start working them into fabric[0] a (python lib) script. I keep all of this in a private git repository.
My older brother taught himself to program at 36. He was a 3D artist before, he had four kids and a wife and a full time job. He spent evenings and weekends building things for his wife's interest in photography and started blogging about his experience learning. He now runs a very successful company and completely changed his life inside of 3 years. He's not the best programmer, but he focused on the work and the assets that he had that were different from people who might be the "best" programmers, that edge is a huge asset.
I've been programming since I was 12 so it's hard for me to fully relate to starting new. Now at 35, I think the thing that people thinking programming is hard later comes from thinking of it like learning to paint or something. One unique aspect about programming is that it's a force multiplier. Once you grasp something, you don't need to reproduce it, you have it and you use it to prop up the next thing.
I'm biased towards python, but experience tells me it's one of the best starter languages because of it's flexibility. Whatever you're working on will always need a web portal, Django[1] is amazing. You can get started quick and python will allow you to do whatever crazy thing you dream up as well.
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I've done a reasonable amount of programming mentoring and four things I've found about having limited time to immerse are:
1) Do things you think are fun! It doesn't matter if it's "relevant" to your track, learning to make it play is vital.
2) Give yourself easy wins early and often. If you find yourself stressing about not getting something, put it down and find a way to get something out quick. Once you have a win, take that new confidence back to your rudiments.
3) Never underestimate documenting your process and sharing it. Blog, draw your problems on paper and in a graphics tool, and keep a physical journal.
4) Try to wrap your head around that the feeling you have now about not knowing IS the state of being a programmer. As you get down the road you will be moving into the exact same state with a new "bigger" things. Something that does change is being able to tab into the sense of discovery and wonder easily. Enjoy it!
I believe in you! You got this!
[0] https://www.fabfile.org/
[1] https://www.djangoproject.com/