Transistor controlled LED ring and help with resistor calculations

I would read this:

Also LED current calculator:

http://led.linear1.org/1led.wiz

I believe connecting LEDs in parallel is a bad idea. I can't help thinking that putting a few in series kills a few birds with one stone. For one thing, you don't need to drop 7.15 V any more, thus saving on quite a lot of heat.