The understanding of "silent cycling" (of the sort Dave nicely describes in his writeup) is very important to people who come in seeking to enter the "planted tank hobby" and is also very important as a powerful learning experience for all who seek greater understanding within the hobby as a whole.. BUT, it can be a bit of a red herring for beginners who just seek to learn how to start up and run what I call a typical "community tank" and get through their first year or so. (I feel you fall into this category because from your tank pictures in this thread you have nowhere near the plant density that Dave is discussing in that article.)
The first thing to understand is that the term "planted tank" can have a special meaning in the world of the aquarium hobby. Many beginners think this just refers to a tank with some live plants in it, as opposed to artifical or no plants. In my opinion it refers to what is almost a whole separate hobby which, at its more extreme, involves hundreds more dollars/pounds of specialized equipment and supplies (bear with me here, planted people) and can be much more focused on the plants than the fish. One such branch of the planted hobby for instance involves pressurized CO2 tanks, regulators, diffusers, high throughput filters, special lights, special fertilizers and the like.
Now, to be fair, the reality of plants in aquariums is really a continuum from simple to complex with several major branches or approaches to success, certain ones popular with certain individuals at any given moment. Hopefully all beginners who want to will eventually learn good practices that bring them success with plants, and virtually all the info that the planted folks can share helps us to that end. However, for the rank beginner trying to have a successful startup of a first year "community tank" (for lack of a better generalizing term, lol) I still find the true planted tank topic to be a tiny bit too much to handle, just sometimes pushes one over the top in the number of new things to be absorbed. (and I'm one of the ones guilty here of introducing it, lol, by talking about the algae, sorry!)
Anyway, there are much simpler ways of having a good amount of success with the live plants in your first tank without jumping in to the full complications of the planted tank hobby (not that there aren't people who do indeed come in wanting to do that and that's ok!) I'd focus on your fishless cycle and getting the full learning of biofilters and a beginning on the art of making stocking plans and of learning good freshwater maintenance practice and just take on small bits of learning about plant care.
~~waterdrop~~