design considerations

I have been playing around with LEDs and japanese lanterns and have made up one using an lm317 regulating at 4.5V and switching 5 arrays of 3 5mm LEDs each randomly randomly with a microchip with we use in our family room a a nightlight. The lantern has been run on 6 and 7.5V wall warts I had in the junk box.

I'm now looking at coming up with another circuit that will use 4 X 1W star LEDs

What is more important when regulating the power? Voltage or current?

At present I have a circuit with an lm317 regulating voltage to 7V. Using an online array wizard and specs for the LEDs I have two series arrays (2 LEDs each) arrayed in parallel as per several wizards. Resistors are correct.

Is there a better way to set this up?

You can use that LM for current regulation too, which would be much safer for high power LEDs. 5mm and to some extent high-flux (superflux, etc) LEDs do alright with voltage regulation and correct resistors, but power LEDs use more current, so errors are much larger.