Sorry again, I realize I'm dragging up an old thread... but I hear this question a lot and nobody ever answered here.
Don't worry about "getting to the age I won't be able to work up" - that may apply to the big leagues, but not so much to the local level.
If you are under driving age, you'll need to get an adult's help - at least for getting you to the track. And if you'll race you'll need written permission from your parent(s). Some tracks may require a copy of your birth certificate, and some may even have a minimum age before you're allowed to race there. Decide which track(s) you want to race at, and ask them.
It is possible to start racing in cars - usually a lower class like Ucar, although it depends upon track rules and your budget. There are 14 year olds driving late models and sprint cars... but they didn't start there, and they have a lot of support usually from people already experienced in racing. I prefer kids start in karts. You can learn a lot about racing without so much risk and expense. Although you can field an Ucar and possibly other lower class cars cheaper than a kart, you can carry a kart in the back of a pickup truck or van whereas you'll need a tow truck and trailer for a car. An up-to-date kart can initially be more expensive than a lower class car, but the kart's weekly costs and maintenance is cheaper. By the way, a lot of big league drivers started in karts.
You could start in a Bandolero if they race those around you and you can arrange transportation. They're essentially overgrown karts with full bodies. Check them out via 600 Racing.
After deciding on your first racing vehicle, you need to think about how far up the ladder you intend to go - and start planning. I'm not sure what you mean by "I don't even need to be a big name", but I assume that you want to eventually be able to win and wouldn't turn down a professional ride if you got good enough to earn it. There are a lot of us that think that way...
At the local level many racers start in karts or a lower car class (usually 4 cylinder engines). Then the progression is to cars that started as street cars (6 or 8 cylinder), followed by purpose-built race cars (limited late models, IMCA modifieds, etc.), followed by full late models or modifieds and even super late models. Generally drivers get experience in each level of class, and demonstrate they're safe and competitive, before they move up another level - but if your budget allows you can skip a class level or two.
For the professional level you'll need to work yourself into a local late model as soon as you can, and win races and preferably a track championship by the time you finish high school. Then you need to get into a touring series and run up front in that, probably before you're 25. At that point you need to get into a series that races at the same tracks during the same weekends as the big boys do (NASCAR, IndyCar, etc.), and run well in it so hopefully you can impress a car owner. Doesn't hurt to bring along sponsorship dollars too. It'll be tough since there are only a few seats in the starting grids of professional racing (compared to hundreds of talented drivers who could race there). For now don't worry about all of that. I'm not trying discourage you - just trying to give you an idea of how hard you'll have to work to get to the professional level.
If your budget is low (like most of us) I suggest buying a used racing kart and starting there. Run in one of the "stock" motor classes - due to your age they'll probably require you to run in one of those, with a restrictor plate. The newer the kart the more competitive it should be, but you can learn a lot without having top flight equipment (especially about your mettle since racing with older equipment can be frustrating sometimes). You can find a lot of help on web sites for racing kart shops and parts suppliers, and at Bob's 4cycle.com.
By the way, it can help a lot if you can make friends with somebody who is already racing. Hang around their shop, ask questions, go to the races with them, get them to show you stuff, get them to help you with your own vehicle, etc. They can shave years of mistakes and wasted money from your own racing career.
