You want at least one stem. Once you have that, buds will form creating more. To help nature along, you can even cut the ends off new shoots causing them to split again. The main thing is to start with a healthy plant.

Fertilizer should not be used as a gas pedal to increase growth or suppress it. Fertilizer should be applied sparingly and then only to maximize plant health, not as a growth regulator.

One thing that is a good growth regulator is sun and shade. Sun causes slow growth and shade causes elongated growth but inhibits flower bud production. A healthy plant will grow well. Then pinching or pruning can be used to cause branching or to arrest rapid growth so the rest of the plant can catch up.

To answer your question, there appears to be a correlation between roots and branches, but it is not perfect. Seldom do you see a plant with problems on just one side or one branch. The time you do see that is in times of drought when one side or stem will die back.