LED driver: how to choose current and voltage?
A schematic would definitely help.  In general, LEDs don't regulate the current themselves, so you'll need a way to bias them.  Most simply this is done with a series resistor.  For instance in your group A with 3 LEDs and 3V forward drop across them, would give 9V across the LEDs as you mention.  You'll need the regulated voltage to be greater than that, let's say 10V for starters.  This would give 1V drop across the series resistor.  Choose the value of resistance to set the current.  

The higher the voltage used, the less susceptible the circuit is to differences in component parameters, but will dissipate more power.  With that in mind, you'll have ensure that all parts meet the power requirements as you mention 1A through the LEDs, which is quite a lot using this method.  With that amount of current, maybe consider using an LED driver chip.