Planning is a good thing
To build the best gravity powered race car that you can, you'll have to start with a plan. Your best bet is to draw something up. Even if it's some scratching on a napkin it will be better than starting without a plan. Draw the design of your gravity racer and start planning out how you want it to look. Some important features to think about are:
Wheels are probably the most important part of your gravity racer. There are a number of different options for different budgets. A cheap solution is to use bicycle wheels. This will also make your steering cheaper and easier. Bike wheels are fast off the line and have good, inexpensive bearings. The downside to bike wheels is that they can't take the stress of high speed turns. If you are racing in a straight line then bike wheels are perfect. If you plan on taking hairpins at over 40 mph, it's not going to work. Trust me, I've done it.
A more expensive but more robust method is to use wagon wheels from somewhere like Lowes or Harbor Freight or go-kart wheels from a go-kart supplier. Both of these will require you to either design spindles for your steering or buy pre-made spindles. The wheels will stand up to more abuse though and can take high speed turns with ease.
The second most important part of your gravity racer are the brakes. You won't go anywhere without wheels, but you might go somewhere you don't want without brakes. There are a number of different brakes available. Perhaps the cheapest and easiest type is a scrub brake. Scrub brakes work by something rubbing against one or more tires to slow the car. This is often a 2x4 pushing against a rear tire. You can put a handle on it and place the fulcrum next to your seat so that you can pull the brake by hand, or perhaps connect it to a foot pedal. If you went with bike wheels, a great brake option can be to use standard bicycle brakes. You'll need to get bicycle brake levers which can be mounted on the steering wheel. I've use bicycle handlebars for steering wheels many times, which helps to connect brake levers too. Lastly, you can spend more money for nicer brakes such as disc or drum brakes. These can be purchased from go-kart suppliers and specialty automotive stores.
Frame and Roll Cage:
Your frame is what keeps your car in one piece and your roll cage is what keeps YOU in one piece. Your frame can be made out of anything sturdy, from 2x4's to pvc pipe to metal tubing. Conduit pipe is a cheap form of steel tube, but you should be careful welding any steel that has be galvanized with zinc as the fumes can be toxic. 2x4's are easy to bolt or screw together, and pvc connectors can make building a frame a piece of cake. You'll want to make sure your roll cage is goes up over your head to protect you in the event that your gravity racer rolls over, such as in a steep turn. A roll bar, or a single bar going up one side of the car, over your head, and down the other side is the very least, but a more robust roll cage that protects your legs and the back of the car is even better.
Just remember, gravity racing is all about fun, but you can't have fun if you haven't been safe first. Always keep safety in mind when designing, building and driving your gravity racer and you should have fun in your race car for years to come!