There's a
lot to read
here and further into the thread are all the details of the ultimate, cheap lighting option.
Unfortunately, good quality off-road lights and affordable budget don't often feature together.
I can highly recommend the Hope vison 1. Some people don't rate them but, IMHO, they represent excellent value for money and have a long burn time if not on full power.
In fact, I rate them so highly that I bought a second shortly after buying the first for use ah a helmet mounted light
Again, they are not rechargeable but of course the advantage is that if you forget to charge them, or your charger fails, you can just nip into a garage and pick up some spares.
I use high capacity rechargeables and have found them to be outstanding and also carry spares in my saddle bag to give me massive runtimes. Far in excess of what my legs give me anyway