However, it's shooting off little suckers at the base. Do I need to remove those?
I didn't know that.http://homeguides.sfgate.com/grow-suckers-banana-tree-34085.html said:Side shoots called suckers grow from the stem of the main plant, also known as the mother plant.
When carefully removed from the main stem and replanted in the ground or in a container, a sucker can develop into a new banana plant...
Removing excess shoots from your main banana plant will encourage the plant to focus on flowering and fruiting. Cut off all unwanted shoots as you notice them.
source