You have a tough but worthwhile goal. It will be expensive and difficult, so don't let it frustrate you. It is attainable with enough work and perseverance, and maybe some luck.
As others have already posted, there is an age bias about what experience a racer is expected to have. That can be leapfrogged via hard work and talent. Realize that you will be competing against guys and gals who have been racing since they were kids (and already have resources supporting them) so you will have to out-work and out-talent them. Can you do it? Only trying and racing will tell.
Start with something that you can afford, in a lower level program support class. In the U.S. that would probably be a 4-cylinder or 6-cylinder car. Believe it or not, there are many of these that are cheaper to run than a kart. But karts have their plusses too, so if they are convenient to your area go ahead and try them. Or take your street car to an autocross event.
It is a good idea to start learning how to build and maintain race cars, and how race cars work. You will be able to give feedback that will make your car faster, which your crew and owner will appreciate. Some of the classes are college level science. You don't have to become a college graduate, but sometimes that kind of effort can separate you from the pack. Learn to become comfortable speaking to strangers, to business owners, and to large crowds.
If you intend to make the big time, you cannot spend too long in your beginner class. Just a couple of seasons in order to learn the basics. You need to progress up the ranks of your local track to eventually the top class - where you need to become a frequent winner. How do you do this? Impress car owners with your talent - both on the track and in the media. Learn to land and hold onto sponsorship, attract talented mechanics, and build a racing operation.
Once you're a local hot shoe, do not delay looking for touring series races were you can participate. You want to go where bigger-time teams and car owners will also be there and can see you, such as ARCA support races on NASCAR track weekends or USAC races with multiple classes. Again you'll have to impress them with your driving as well as off-track performance... you may also have to bring some money with you. You might also move to where your preferred series has a high representation. For NASCAR that would be Charlotte, NC. For other series, like F1, you might have to pick a team that you'd like to work for and move near their shops. You will need your resume, to bang on doors, and to be prepared to start out sweeping floors. There are a lot of other racers doing this same thing - again you will have to beat them out with good attitude and talent and hard work.
Sometimes top level teams or series have development programs or challenges. Try to get into one if you can (they will more likely invite you if they have seen your past racing success). These programs are usually specific to a certain racing series - for example, NASCAR's Drive for Diversity Program helps women and minorities - take advantage if you can. Some NASCAR teams have their own development programs. F1 also has a driver development program. You'll need to decide which top racing series is your goal, and seek out programs that relate to it.
As you get older the age bias will work against you more and more. But don't take shortcuts (get in over your head) because that can be deadly. Realize that only 40 drivers maximum start a NASCAR Cup race, only 20 start in F1. You are not a failure if you don't make it there. Many successful racers make good livings driving for short track racing sanctioning bodies like WoO and Lucas Oil and ASA just to name a few.
Bottom line: most big name racers admit that hard work and talent and being in the right place at the right time shaped their careers. Start with something manageable for your experience and budget, work to become a contender at that level, then quickly move up to the next faster class (and repeat) - including moving up whole series. When you are able to tour, get yourself into races where the big boys are so you can get noticed. Develop an understanding of how engines and chassis work so you can provide valuable feedback. Develop social and marketing skills that attract sponsorship and support.
It will be quite the adventure, and sometimes the path takes you where you weren't expecting. Embrace it.
