What should a regretful student who is caught plagiarizing do to move forward?
You sound quite naive about what constitutes plagiarism or academic wrongdoing at the university level (in particular the thought that paying for the code makes it okay or even less likely to be caught is pretty much exactly wrong).  But this naivete is quite well explained by the fact that you're a high school student.

It's great that you realize that you did something seriously wrong: I agree with you.  But you're not a sociopath: rather, you are a teenaged minor, and your behavior is well within the normal operating parameters of such entities.  Many (perhaps most) minors do at least one really stupid thing that if they were an adult would get them in real trouble.  But unless their actions cause irreparable harm to others, the adult world tends to be forgiving: there has to be a time in which you can make mistakes and learn from them.  

I think it is very unlikely that your actions would cause the university in which you've been early admitted to rescind its offer.  This is on the border of being so unlikely as not to really be worth worrying about...but someone in your situation is going to worry.  Here's how to allay your concerns:

You should go to your professor and explain very calmly and honestly everything that happened.  Your position should be that you are thoroughly repentant and will not contest whatever penalty to your course grade you have received.  You have just one concern: you don't want the academic dishonesty to appear on your transcript, because -- be honest -- you think that might jeopardize your collegiate career.  If it comes to it, you should make clear that you would rather get a failing grade or an unsatisfactory withdrawal from the course.  (This is a difference between your situation and that of most normally enrolled university students.)  If the professor is not willing to agree to that on the spot, then you should talk to others -- in particular, to your parents -- about how to proceed next.