The type of thumb and finger picks you use can have a big effect on your tone. Bending the picks or not bending the picks will affect the tone as well. I recommend experimenting with pick types, gauges (thickness of the pick), and bending the picks.
The thumb pick you choose should not catch the string where the lip hangs over your thumb. If this happens, I recommend cutting off the part of the lip that is hanging over your thumb and catching the string. You can do this easily and it should not affect how well the pick stays on your thumb. This is a flaw in the pick, not you.
Generally, a thicker pick provides a mellower and darker tone, while thinner picks have a brighter tone. Since the banjo normally has a bright tone, I recommend using thicker picks. When bending picks, most people put the pick on and then push their finger down and roll it forward until the pick shapes around the tip of their finger.