Your first paragraph ...The art of choosing just the right chord progressions is an often overlooked aspect of writing a song, particularly for beginners. So much of the focus is placed on the words and melody that the chords are just kind of left behind.
The melody and lyrics may well be the most important aspects of a song, but that doesn't mean the writing of the chords should be given any less attention.
If you are content with just playing the same four chords throughout, your song will most likely turn out sounding rather lifeless and unimaginative.
There are, of course, exceptions to this. U2's “With or Without You” springs to mind. But U2 are a great band. They've learned the art of playing with exceptional dynamics, so they can play those same four chords and make the song sound fantastic!
I believe the melody and lyrics should be given priority over the accompaniment, but an interesting chord progression will serve as an important structural support for your melody.
The key to making a simple, repeating melody interesting is to incorporate a changing chord or bass progression beneath it.
You can have three or four lines of the exact same melody, but by trying out a few different chord progressions, you will make that same repetitive melody suddenly sound exciting. You can even change keys. Using relative keys is an easy way to do this.
Say you've written your song in the key of A major. Try playing the verse in the relative minor which is F# minor, then going back to A major for the chorus. Now your song has taken on a whole new dimension!
Or write your chorus in a completely different key than your verse. If you've written your verse in the key of A major, try modulating to B major for the chorus. The result will be exciting and triumphant-sounding!
Want to be a bit more ambitious? Try this:
In this example of a verse progression I'm playing the chords Am, F, G, Dm. It doesn't matter about rhythm or tempo, but let's just say 4/4 with 4 beats per chord.
Play this chord pattern twice, which will be the first half of the verse. For the second half modulate the entire pattern up a step and a half. Now the chords are Cm, A♭, A♯, Fm. Modulate the melody along with the new key and listen to your song explode with life!
Now all you have to do is find a way to get yourself back to the original key of Am for the chorus (unless you want the chorus to be in a different key altogether). Spend a little time here and there studying music theory and you won't have any problems with this!
You would do well to learn some music theory, as it will give you the ability to write with added depth and imagination.
If you play an instrument you've already delved into a bit of theory, even if you don't know some of the terminology.
Delve a little deeper. Teach yourself to play familiar tunes in unfamiliar keys. Learn stuff like the Circle of Fifths.
Make a point of learning a few new chords each week or so and writing a chord progression around them. You may think you'll never use a minor sixth chord in your punk-pop composition, but there is a time and place for everything.
Even if you don't ever use that chord, you will gain a little more understanding of music theory just by learning to play it and what other chords might go nicely with it. With each new bit of knowledge you acquire, you will become a more well-rounded musician.
The more well-rounded you become as a musician, the more tools you will have at your disposal that will help you to become a better songwriter.