Lights

Hi

I need some lights for a mountain bike for the winter and I'm a bit
confused about those on offer that seem to range from about 10 pounds
to over 600 and all of which seem to describe how bright they are in
different ways.

My journey to work is about 4 miles along an unlit disused railway
line (a rough surface but not extreme off road) and about half a mile
at each end on the road which has street lighting.

Can anyone recommend me some lights please that are powerful enough to
use along the unlit part (how many watts / lumens do I need for this?)
and also legal for the road, and given this as cheap as possible.
Ideally they should be easy to remove from the bike when not in use
and use a power source that can be recharged easily.

Some of the lights I have seen use LEDs, some traditional lightbulbs.
Is there any advantage to either?

Thanks

Richard