It sounds like the question has already been ansered but I figure I'll post some ideas that people might find helpful.
The first thing I do is i write it in roman numberal notation. So just say we have: C F G7. C is the root and major so it is I. F is the fourth note of the C major scale so the F chord is IV, then G is the 5th note so the G7 chord is V7. So now we pick any key we want and we replace C with the root, F with the IV chord and G7 with the V7 chord.
here is a table of keys.
So we can do the key of G and the chord are: G, C and D7 (i just noticed the major triads are wrong on one of them but the keys look okay), or i can do F, the chords are Bb and C7. Now just say you figure out that the key of F best suits your voice. The F note is 8 half steps above C. What that means if you rasied all the notes in the C major chord by 8 half steps you get the F major chord, if you raise all the notes of the IV chord of the F major scale you get the IV chord of the C major scale. So if you capo the 8th fret when you play the shape of the C major chord you are in actuality playing a F chord, same with the other two respectively.
Lets say you don't want to capo the 8th fret, that's why I brought up writing the chrods in roman numerals: I, IV, V7. We can play any key w/o using a capo, we can play the song in F major by playing the chords: F, Bb and C. By doing that instead we are changing the shapes of the chords, and we can use a capo in order to pick different shapes and maintain the same key if we want. For eg C major has 2 thirds in it and E major has 1 third (they also have the intervals in different orders which effects the sound) so depending on what sound we want we might rather the C shape or the E shape.
So lets say the key of F really fits your voice, the chords we want are: F, Bb and C7. The key of F is one half step higher than E, so if we raise all the notes of the key of E chords by 1 half step we get the key of F chords.
Another example, just say we have a song in the key of C: C, Dm, F. In roman numberals its: I, ii, IV. Just say b/c of the way C is used the way it sounds is too weak sounding, just day the Dm doesnt use enough strings for the song, and so on for F the reasons dont matter, just say the shapes in C aren't ideal here. But just say the chords in G are very good for the song, them I, ii, IV in G are G, Am, C. Lets say I'm gonna play G 320033 to make it stronger, and the usage in the song for the IV is good to have a prettier feeling that C offers and not F. So we like those shapes but we don't like the key of G. C is 5 half steps higher so if we raised all the notes of G, Am and C by 5 half steps we get C, Dm and F respectively. So we capo the 5th fret play the G, C and F shapes and we have the key of C and the sounds we want.
In short you can use a capo to change the shapes of the chords even if you dont want to change the key. Did anyone find this post helpful? Sometimes I feel like I write these and then if no responses its like no one read it found and benefit in reading it.
If you learn how to play songs, then you learn songs. If you learn how to improvise, then you learn music.