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Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
For any progression, what you really need to do, to understand the key, and the key's notes, is to follow these steps. I'll take your G-Dm-Am-C looped progression as an example.
1) Identify the root. This is pretty much the first thing you have to be able to do as a musician. Other words for root are key note, home note, 1-chord, "what the song is in", final resting place, foundation note, fundament, base, home base, etc. In your little progression the home note is G. This is pretty uncontroversial. The progression starts and ends on G (because it's actually G-Dm-Am-C-G). So G is the root. If you struggle to hear that with absolute finality, then try listening to more music and practise listening to where the music draws to a close. It's not always the first chord, but it often is. It's normally the last chord, but sometimes it's not. In your progression it is. The way you've written it looks like the last chord is C, but it's not, it's G. Because it returns to a final G after that C. It's sort-of like this:
G-Dm-Am-C / G-Dm-Am-C / G-Dm-Am-C / G-G-G-G.
You should be able to hear those chords going round and round and hear where home base is and correctly identify it as G.
2) Identify the "tonality". There are 3 choices: major, minor, or ambiguous. The way to find out is to see what your G chord is. Well, you've already said, it's G, not G minor, so you're in a G major tonality. It could still be ambiguous, so to be bullet proof, you could look to see if there are any G minor notes in the rest of the chords. The major / minor determining note is the 3rd. In G, that would mean a B for G major, and a Bb for G minor. You just have to know that. Now, when you look at your other chords to see if any of them deploy a Bb, none of them do. Actually none of them has a B or a Bb - the notes just don't exist in Dm chord, Am chord or C chord. But importantly there's nothing to give a hint of G minor. So it's not ambiguous. You're in a G major tonality.
3) Establish the chords of the progression, agnostic of key. You're playing 1 chord, 5 chord, 2 chord, 4 chord. You can just count up the alphabet to find that out. Now, you're playing the 1 as Major, the 5 as minor, the 2 as minor and the 4 as major. So the progression is a 1524, and written in Roman Numerals, it's I - v - ii - IV. (the Capital letters denote Major.
4) Identify the scale that fits with this progression. You have to ask, are you in bog-standard "Major" (AKA "Ionian mode") or one of the other major modes?
OK. There are two other major modes besides Ionian. They are Lydian and Mixolydian. Which are you in? Well, there are some clues in your chords. You can't be in G Ionian, because G Ionian has a V chord, not a v chord. And you can't be in G Lydian, because that has a raised IV chord (as well as a major V chord). Whereas what makes mixolydian special is that it has a minor 5 chord - in other words, a v not a V. (This is just stuff you have to learn.) So your progression is in G Mixolydian.
The notes of G mixolydian are G A B C D E F G. (yes it's the same notes as C major, or B locrian (which is horseshit so put it out of your mind), or A minor. But those facts are irrelevant. Because you are in G, not another letter.)
And the chords of G mixolydian are G Am Bdim C Dm Em F and G.
As you can see, I - v - ii - IV fits perfectly with it. I've bolded the chords above to prove it.
5) Noodle away. There you are. G mixolydian it is. If you noodle in G mixolydian throughout that progression it will sound fine. Of course you can deviate from that to create interest and tension. but the default notes are G A B C D E F G.
Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.