There are "be seen" lights and "see" lights. The cheapie lights will help you be seen by cars, but won't project far enough out to light your way (unless you roll at a walking pace).
If you want serious lights, NightRider, CygoLite and high-end Cat Eyes are the way to go.
I do a LOT of night riding, and for a front headlight I would get one that is AT LEAST 200-300 lumens (about 1/3 of a car headlight). I know people who have 1000 lumen lights on their bicycles but I think that's overkill. I am currently running a NightRider Lumina 700 light that's 700 lumens at the highest setting. I usually run on the lowest setting (150 lumens) but have the option to go brighter when needed. It's a tradeoff between brightness and runtime. I got mine for $70 on a Black Friday sale. There are more affordable versions such as the 250 lumen one.
Tail lights are every bit as important. If you ride on the streets at all, cars will probably see your tail light first. I have two types, Serfas Thunderbolt and Cygolite Hotshot. There's a white version of the Thunderbolt and I've seen people use them as headlights (although they are more of a be seen that a see light).
All of these lights are self-contained units with rechargeable batteries that are USB rechargeable which makes them very versatile. They also have attachments to fit many different diameters of bicycle frame/handlebar tubing.
If you look at the different sites like REI you will find there are also combinations of a headlight and tail light. For a serious "starter" kit, consider something like this.
You may check your local bike shops and see what they have on sale. This is a good time of year since for sales because few people start riding now at the end of the summer so bike shops put stuff like this on sale.