Things to think about includes questions such as; will there be children around that may touch the light? Does the light need to be left on throughout the night? What exactly are you using the light for and how much light do you really need? Will you be frequently moving the light or leaving it in one position?
Answering some of these types of questions can help you to make a decision of the right light for your situation. There are two basic types of lights available. That is those that run on liquid type fuels (such as kerosene, paraffin, LPG etc) and electronic lights that run on batteries. You might even come across lights that can operate on more than one fuel source. Bu a rule of thumb, the lights that run on liquid type fuels tend to burn brighter, but running costs are often higher. Another consideration with liquid fuel type lights in the danger involved should a lamp be bumped over or played with by children. Liquid fuel lamps can also let off an unpleasant odor which some people have even suggested could be toxic (especially to children).
Modern advances in technology has seen a range of very long life, safe, inexpensive and reasonably bright options. Of the electronic lights, there are those which have a traditional incandescent (filament) bulb and of course modern LED lights. Lights that run an incandescent bulb are usually much more draining on the battery power than LED lighting options. There are even LED options available which can be charged by simply winding or cranking a lever and some which you can just shake the entire light to generate some power.
When choosing a light type, think about how readily you can get more fuel to power it if you run out. This applies for electronic lights too, as if you run out of batteries where you can not easily get to a shop, you will be literally left in the dark. It always pays to pack some emergency extras.
The actual size and weight of the light should be thought about. Are you planning on taking the light walking with you? If so, then a liquid fuel type will probably be too heavy and potentially dangerous. If you are walking in the dark, perhaps something like a headlamp would be best suited for that situation, allowing your hands to be free.
Most people agree that when camping where children are involved, it is always safest to opt for electronic type lights which minimize the risks down to almost zero. None of us want to see children being burned by lights.