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This is a typical circle of fifths chord progression.
My question is how do we choose the chord to be major, minor, or diminished along with the progression:
A -> D -> G -> C -> F -> B -> E -> A?
Why is that:
Am -> Dm -> G -> C -> F -> Bdim -> E -> Am?
What are some golden rules to determine the major, minor, diminished along with the progression?
The image is from this video.
The reason it's Am Dm G C F Bo E is that they're all diatonic - their notes all belong to the same key - A minor. That way, they all sound like they 'belong' together, which, of course, they will do.
They don't have to be those minors, majors, etc. Am D G C F B E works almost as well. Obviously it's the circle of 4ths, which crops up in plenty of different music - and the ii>V>I that occurs in so many pieces is part of that sequence. The preceding chord is the V (or v) of the next, hence the 'dominant' label.
Choice of chord? Depends on the melody - the notes from that will usually need to blend with those of the accompanying chord, so one will dictate what the other could be.
We can tell you which flavour of each chord to use if you want to keep the sequence diatonic to one key. But there's no particular reason to do that!
The strength of the progression lies in the 'cycle of 5ths' bass line. I suggest you maintain the same harmonic density - all triads, all 7th chords etc. - otherwise it can sound a bit disjointed. Apart from that, there are no wrong answers. Musical composition involves choice, otherwise from any given starting chord there'd only be one 'correct' path. So choose!
You can choose the chord types Am -> Dm -> G -> C -> F -> Bdim -> E -> Am for A -> D -> G -> C -> F -> B -> E -> A because all of those chords fit in A minor (with no tonicizations and no modulations). In A minor, you can interpret those chords as i -> iv -> VII -> III -> VI -> ii° -> V -> I.
You get more flexibility by allowing tonicizations and modulations (especially since circle of fifths progressions often involve both of those). For example, you can use B instead of Bdim in the above chord progression so you use V of -> V -> i instead of ii° -> V -> i.
Put accidentals on some of those chord labels in the skeleton and you can come up with some spicier chord progressions while still using exclusively common practice period harmony. For example, you can use A -> D -> G -> C -> F -> B♭ -> E -> A for I -> IV -> V of -> V of -> V of -> ♭II -> V -> I. There's also the similar Am -> D -> G -> C -> F -> B♭ -> E -> Am for i -> IV -> V of -> V of -> V of -> ♭II -> V -> i. For a different sound, there's also A -> D -> G♯ -> C♯ -> F♯ -> B -> E -> A for I -> IV -> V of -> V of -> V of -> V of -> V -> I.
