When I was looking for a kit for my bike, my main concerns were quality, support after the sale, and price.
As the saying goes, you can have things 2 of three ways: good, fast, or cheap-but not all 3. You can find high quality components at good prices, but you'll have to do all the wiring, and figure out how to install it on your bike. You can get good components with pre-made wire harnesses that make for a quick and easy install, but they cost more. And on, and on...
You also need to look for a kit based on whether your bike makes power for lighting already or not. If you're riding a bike with a headlight and taillight on it already, it does*. If you have a motocross bike, and/or you don't have any lighting, your bike very likely does not make power for lighting.
*If you have a bike with lights already, you can skip this section and scroll down to "Bikes with lights on them already".
Lighting Coils/Stators:
A bike makes power for lighting with what is called a lighting coil or lighting stator. I'm no expert on stators, so I won't be getting too deep into the theory behind how they work.
If you have a bike that doesn't have lighting, you have 2, maybe 3, options. An internal aftermarket stator with lighting outputs added, customizing your existing stator to add lighting output, or a battery.
Battery power:
If you can't find a stator for your bike, or just one that you like/trust, you can run most kits 100% on battery power. Now, understand that you aren't going to be able to ride around all day with your lights on when running on battery power, unless you have room to mount a pretty large battery.
The battery type you want to get is called Sealed Lead Acid, or SLA. These batteries don't mind being discharged and recharged over and over. Just be careful not to completely discharge them down to nothing or, as with many types of batteries, it won't take a charge anymore. You might also be able to get away with running a "battery pack" similar to what goes in an RC car, if you only want the kit to pass inspection and will only turn the kit on for a few seconds while connecting from one trail to the other. If you plan on spending more than 5-10 minutes at a time on the road, I'd spring for the SLA battery. Don't try to use a motorcycle or car battery for this. Motorcycle batteries aren't meant to me deeply discharged and recharged over and over.
The 2 most important things to look for when choosing your battery (other than getting the correct type) is voltage and amp hours. Most people know what the voltage rating means (12V, 6V etc). Amps or amp hours can be a little less obvious. You will almost certainly need a 12V battery, unless you find a kit that runs on 6V. You will also need to get at least 5 Ah rated battery if you are using non-led lighting. You can get away with 2-3 Ah if you are running all LED lighting. If you Google "12V 5 Ah" you'll see lots of results. I ran down to the local Radio Shack and picked up a 12V 5Ah SLA battery for about 35 bucks. I liked this battery because it is pretty small and will give my kit a good solid hour + of run time. It will run longer, but power would begin to drop off. I've run for an hour and 10 minutes and my headlight was just barely beginning to get dimmer.
Here's how to figure out what size battery you will need, and how long your kit will run on batteries of various Ah ratings:
Add up the combined wattage of your headlight and tail/brake light. (35 + 35 = W)
Divide the total wattage by 12 (W / 12 = )
The number you get is how many amps your kit will use.
For example, my kit has a 35W/35W headlamp (35W for the low and 35W for the high beam * Make sure that you account for the highest wattage, some hi beams are double the low beam i.e. 35W/70W) and an LED tail/stop lamp. For my LED tail lamp, I just added 1 amp to my total, which is WAY more than it will draw, but that will account for the occasion horn honk as well.
So: 35 dived by 12 = 3 (roughly). Add 1 amp for the LED/Horn and you have 4 amps total.
A battery with a 4 Ah rating will, theoretically, run a 4 amp load for 1 hour. A 2 amp load for 2 hours, 1 amp load for 4 hours, etc etc. So in order to be sure I have a solid hour of run time, I bought a 5 Ah battery. You can buy as big a battery as you wish and you'll get more and more hours of run time. If you buy a 12V 20 Ah battery, you will get about 5 hours of lighting per charge. If you have the room to mount it, and the budget, no problem. For a 10 minute drive down to the local trail, 1 hour of run time is more than enough for me. It also gives me a little extra light for the "unexpected".
One other bit of info: Some batteries are rated in mA hours. For example, 12V 3800 mA. Just divide the mA rating by 1000 to get the Ah rating: 3800 mA = 3.8 Ah. A 12V 800 mA battery = .8 Ah.
Once you have your kit, and a way to power it, see "Installing a Light Kit on your Bike"
Bikes with lights on them already:
If your bike has lights already, you can pick out your kit or components to make your bike street legal You can also use your favorite search engine to find more information on making your street legal with just a few inexpensive parts. If you aren't comfortable with soldering and bike wiring, a kit may be a better choice for you. You could even have your local shop install it for you.