PS - Those types of front light are not good for road riding. They need to be turned to point at the ground, or they are incredibly dazzling to oncoming traffic / pedestrians.
Front lights should have a shaped beam with the LED shining down onto a reflector, they are far better for seeing than the normal sorts. Direct beam types are poo, lights in the wrong place, and as mentioned above, extremely irritating to traffic - although most cars are now the same.. so its fair enough but expect blinding high beams if you go with rubbish over bright lights.
These were good, I bought three sets. Loads of light and would last ages and I could go off road at night no problem.
I am not sure if they will be available where you live, but I quite like the Moon Meteor (it comes with a rear light). They are good for riding in urban areas and semi lit tracks. It has a claimed 500 lumens and a nice beam focus. I use mine for commuting, which is about a 45 minute trip and it does that with no problem.
If you are going to be ridding fast off road in an unlit area you will need something brighter.
It depends on what he actually wants it for.
Riding roads/tracks, or off-road mountain biking.
Cheaper lights generally don't have the best beam pattern for either, but will do the job.
I almost miss the lots of light, but not where you really need it aspect, which is why even yet I refuse to use a helmet light for mountain biking!
Road you really want a 'hooded' light, but they're pretty expensive and not many people produce them (I bought mine from Germany, but can't remember the brand right now! Exposure in the UK make road specific lights, but probably not in the price range you want), and it makes a big difference for road riding as it lights up a good distance in front without blinding anyone coming the opposite direction.
The ideal mountain biking beam is more spread out with most light being directly in front, but with enough side spread so you get some light for potential corners.
Halfords own brand lights are generally well regarded and well priced, and you're getting a known quantity. I used one on my road bike for a while, which wasn't ideal on rural roads with traffic coming the opposite way, but I know several people who've used them for mountain biking. I certainly couldn't complain about the performance of the light itself.
I'm still using a Halfords rear light when I need one. If he's going to be doing a reasonable amount of riding on roads, it's worth having two rear lights.
lezyne, are my preferred light now, good battery life, a range of light levels, they do cost a little more but they last years and take a battering, this is reminding me I have actually lost one and its annoying me.
But I also have the set in post 2 and they do a great job too, my batteries died after some time though.
For forest night riding I bought my main light from "Bright Bike Lights" some years ago.
Almost certainly the light unit is generic Chinese Cree stuff - but the battery pack was much better quality.
How & where you run lights makes a big difference btw.
You also really need at least 2 lights....
1. As if one fails, you're in deep sctuck in pitch black on a bike among trees.
2. Main light on helmet, secondary on bars means he has light where he is looking & light where his front wheel is pointing - much better & safer.
Due to cost of expensive bespoke helmet mount lights, I run a "Miners Lamp" arrangement where the separate battery pack is on my bum bag, and the cable run up inside my top and through a velcro loop on the back of my helmet, to the small twin cree lamp (which I tucked under the peak of my full face lid to stop it catching on overhead vegetation).
Bar lamps.... I use 2 cheapo Lidl cree lights. They give enough light as secondary units.
If you teach the lad to switch his main light off and run minimum bar light power when on fire roads to save battery - then a decent 2+ hour night ride is doable without major outlay.
(A rear light can be any small LED... but note the practice off-road in company is to not run a rear light as it'll screw up the vision of snyone behind you on the trail - just use it if he has to ride on the road to get to his playground).