Sadly I don't know the answers to your questions. There are about 150 people listed on the previous four pages, all of them really good drivers. But I doubt any ten of them would agree on the best way to reach the top. I have almost zero experience with autocross and even less in a real kart. I can however give you a few general concepts to think about if you want to get started in racing.
Money
Racing is expensive. When you get to the track, you will find that there are people there who obviously have a lot more money than you. Don't hate them for it. You won't get very far in the racing world if you hate people with money. I honestly believe that anyone who ever gets to drive on a racetrack has too much money. Be thankful.
School
The most important aspect of racing is the skill of driving. Triple adjustable shocks, racing tires, and entire cars will come and go. Your skills will stay with you. Money spent on instruction is usually well worth it. But the costs vary greatly. I see professional racing schools as being higher education. $2000 for a weekend at a professional school may buy you the final skills you need to win a championship. But there are much cheaper ways to learn what the flags mean and how to give a point by.
Track Days:
I would start by going out with a local club racing organization that requires beginners to take their school. Typically this will include classroom instruction and an experienced driver that will ride with you in the passenger seat of your street car. With most of these organizations, all of the beginners will be on the track in their own run group. From there you will advance to groups with less supervision and more open passing regulations. Avoid organizations that do not require newbies to take a school. While yahoos tend to gravitate toward racetracks anyway, disorganized groups attract a higher percentage of them.
Racing
Typically about half of the people who come out to a track day will never come back. Then only half of those that return will come out for a third weekend. By that point you will know if driving is for you. If it is, get in a racecar. Street cars and restricted passing zones are great for getting a taste of things. But, before long your car will rapidly devalue and your skills will level off. Get in a racecar, the cheaper the better.
It may seem contradictory to drive a slow racecar instead of a fast street car. But following the mantra that driving skills come first, it is the best thing to do. Firstly there is the safety. If you're going to push a car to 100%, there's a good chance you're going to go off the track a few times. Every time you go off, and even sometimes when you don't, you roll the dice. Having extra impact and fire protection will allow you to push harder. Secondly, racecars are better for feeling what the tires are doing. High noise, vibration, and harshness, (NVH) levels are considered bad in a street car. But on the track you want all that stuff you can get. You need to know what a car is doing in order to hold it at its limit. A gutted car with hard or solid bushings has fantastic NVH levels. And if you're going to do all that, you might as well go all the way and have a racecar. Finally and most importantly, the rules of the track are different for racers. You will no longer waste expensive track time waiting for a passing zone. If the track is clear it's like the best lapping day ever, if there's traffic it gets even better. You will learn to pass wherever you can, and learn that others will do the same thing. You learn to watch your ass.