I'm no expert on this stuff, I have the ADV monster lights and like how they work. I have two of the Model 30 flood lamps (3 LEDs/lamp, no longer available). I suggest the Model 44 flood lamps (4 LEDs/lamp) or for more output, the Model 60 (4 LEDs/lamp).
http://stores.advmonster.com/led-lights/
For trail riding, a flood pattern is best, but there is a huge variation in beam angles from different manufacturers. The ADV flood is 30* and works well for me. This is for riding single track (2nd and 3rd gear) and forest roads (6th gear). I rarely exceed 45 mph so I don't need a long range pattern. You should see the beam pattern in person to be sure it will suit your needs; don't trust that a manufacturer's definition of flood (or spot) matches what you expect.
Light bars are another good way to go, but the beam pattern is more critical because you don't have the positioning adjustment of individual LED lamps. A light bar needs to be mounted high to avoid fender shadow. Fender shadow means you lose close-in trail details.
Higher draw usually means brighter lights. I use a Skene Design dimmer (DC only) and have my lights at about 40% output during the day which reduces the power needed. At full brightness the battery will run down after an hour or so.
As to wiring I suggest using a Lithium ion type battery (slightly-smaller-than-stock Ballistic 8 cell or the even smaller Shorai). You still have lights if you stall the engine. Use a fullwave rectifier connected to the stator white wire and chassis ground for the input. The output must be floating (non grounded). I don't see any value in using a capacitor for electrical storage.
Some LED units may be able to run on AC current; you would need to confirm this with the manufacturer. In that case you could power them directly from your stator yellow and ground. Engine running = lights on.