what flavor of the chord do you choose??

I have just started looking at playing chords, having just about learned where all the frets are. My question - looking at the chord charts it looks like you can play a D chord most the entire length of the fretboard so which flavor of the D chord do you choose (2-3-4) or (4-5-7) .... ??? I guess it has something to do with those black dots on the music bars. I know a little about music theory but not much. Also if I play a D chord with the dulcimer tuned to DAA is it close enough to play along with someone tuned to DAD or do I need to play the chord starting 3 frets higher than the other person assuming there is enough real estate left on the board? Hopefully I have made sense with these questions or should I take up ice fishing for the winter when the snow isn't deep enough to play in. Thanks everyone - Any illumination will be appreciated.