Keep it simple, have fun, focus on one thing at a time, and you'll progress more quickly. As you advance, you will play more and more at the low end, and the bigger hand effect sound comes from the biggest part of the cup. And this is assuming that you are holding the harmonica with the numbers facing up, with the low notes to the left, like a piano. A couple of great players, Sonny Terry and Paul Butterfield, held the harmonica in their right hand, but they also had to hold the harmonica upside down. There is no advantage to this if you know the correct way to hold it.
Many players use chords on purpose for effect and for contrast to single notes.
Keep practicing your single notes so that you ultimately have the choice between the two. Most likely you are going too fast or trying to do too much. Slow down, take your time, listen to what your doing, and let the muscle memory develop with clean correct single notes. Another reason could be that your lips and mouth are getting tired. Take a break and come back to it after a few minutes.