On the cheap light front - I have had good luck with the Bright Eyes light found on Amazon, I use two of them for the headlamp/handlebar combo (diffuser on the handlebar). It is solidly built, a bit heavy and the handlebar mounting system could be better (I wrap electrical tape sticky side up around the bars where I mount it to keep it from moving around on the descents), but for $50/light it is pretty tough to beat and it is in an entirely different league than the other cheap lights I have seen.
I can't speak to the longevity of the battery yet, but between the price point and the customer service (read some reviews) I have zero regrets. I do put the battery in a metal container while charging to be safe.
Slipped out on some ice last fall and my headlamp light took a direct hit to a rock - didn't even phase the light and no visible damage.