For woods riding I'd recommend flood pattern, you won't be able to see far enough to make use of a spot beam.
It'll also help you to see in a wider periphery when you're turning and the light is bolted to the frame.
Spot beams give you tunnel vision (which is fine for roads and long stretches of high speed driving).
With that in mind, if you're turning to one side you might not notice the tree just outside of the spot pattern until it's too late to change course.

Stock regulator is the only thing you need, so long as it keeps the voltage around 12V.
Doesn't matter what type of lights you want to run.
Make sure it maintains 12V on the hot wire going to the lights and you'll be fine.