Hello @dailin your question and issue is unclear, let’s try to unpick it.
I do not understand.
When you say ‘pick them’ do you mean choose them or do you mean play them as arpeggiated chords picking out the notes one at a time?
Whichever you mean, in the key of C the D is D minor, the E is E minor, the A is A minor.
You do not need to start on the note C, you are correct. You can start on any of the notes. If you are playing over a progression with a few different chords, then sometimes the note you choose to start on will sound great, other times not so great. This is all about exploring, trying, listening, having a go.
I would like to direct you to Justin’s Practical Music Theory course also - it is invaluable.
And to this topic: Basic steps in improvisation - Targeting chord tones using a Chet Atkins beginner lesson