HFMaxi is an actual real life rally driver, so listen to him. I am too but I'm not as successful.
Let me tell you what I did, sort of in order, and the approximate costs for the car and events (including the tires/fuel/hotels/whatever). I'm 10 years out of high school now, for reference.
Autocross: You can do this with a car worth less than $2k. Per-event costs can be under $100 all-in. You don't need to be able to work on your car, but it helps, and it's a good place to learn basic car control and setup. This is where I started. Take auto shop if your school offers it.
Rallycross: Similar costs to autocross, but on dirt. Usually more fun, more seat time, but you pretty much need to be able to work on your car because you will occasionally break stuff. Consider this a requirement if you want to rally later, because you need to know how to drive on loose surfaces.
Formula SAE: If you go to college, this is 100% a must do. Somebody else's money, somebody else's shop, and you will learn to design stuff, fabricate it, and work on it. On a big team you'll be well funded and get to spend a lot of time on one system, on a small team you'll get to design the whole car yourself if you want. Cost is $0 but a ton of time, and you learn more than the rest of college will teach you (about cars, at least).
LeMons/Chumpcar: The car will run you close to $5k unless you can fab the cage yourself, per event costs will be in the $1k-$2k range. Real wheel to wheel racing isn't cheap but this is a good place to learn to fabricate and do mechanical work. It was cheaper when I did it, I don't find it worth the money now.
RallyMoto: If you can ride a motorcycle this is an excellent way to start rallying. A decent bike will run you $2k-$5k depending on how nice you want it, per event costs can be kept in the $500-$1k range if you're not buying new tires every time. Bikes are tough and rarely break. As a RallyMoto rider, you have to do your own navigation and timecards, so you learn what a codriver does while you're at it, which is super useful for having a full understanding of what's going on when you get into a car.
Stage Rally: Trying to do this right off the bat would be like trying to summit Everest as your first hike. It's hard, you can get a car going for less than $10k IF you're a decent mechanic and fabricator, and per-event costs are $1500 minimum and usually closer to $2k-$3k because you WILL break stuff. You also probably need a tow rig and trailer, it's doable without them but risky since you'll need to rent stuff or pay somebody to get your car home when it breaks. I can't emphasize enough that you should get as much practice both driving and working on stuff as possible before you do this, or it will be a monumental waste of money.
The other thing to consider is that each of these is fun when you first start out, in order of difficulty- but if you do stage rally first, all the cheaper easier stuff will seem lame. I definitely recommend working your way up to it. If you want the shortest path that will get you there while still learning enough, I'd say to do all of the following: Rallycross to learn car control, woods riding to learn to ride a motorcycle, a few years of RallyMoto to learn to rally while saving money and prepping a car, then Stage Rally- and by the time you hit Stage Rally, you need a good paying job and a place to work on your car, or you'll burn out and run out of money very quickly.