If you are getting comfortable with the beginning of Sweet Home you should be pretty comfortable working with the D chord.
Try experimenting with removing or moving a finger around while in that chord. You can also moving a finger up vertically to the A string and place it in the 3rd, then 2nd fret then no fret. Do the same on the next string down (D string). You should recognize some of the sounds you get there. I've heard this is called the "D-box" but not sure about that.
Anyway, once you feel comfortable fingering a chord experiment a bit by adding fingers, moving fingers or removing fingers. Sometimes it will sound like crap, other times you'll hear how some song works. You are basically making different chords.