I am a current high school student will to pay up to $200 if need be. I just want to ensure I am publishing in a good journal not one that is a scam. I was considering arxiv but I am seeing that it is not well reputed.
arXiv is not a journal; it is a place to put research which allows it to be publicly available before it appears in a journal, and enables it to remain open-access, at least in some form, after it appears in a journal. If you were submitting to a journal, you would normally put the paper on arXiv as well.
However, it is unlikely that you will even be permitted to put it on arXiv without someone "endorsing" you: see this question. This is true for anyone outside of the academic research community (or even those inside who are trying to post research in a different discipline). It is unusual (though by no means unheard of) for high-school students to produce publishable research, and they are certainly unlikely to understand what is and isn't new or significant, or how to write it up effectively, without some sort of mentoring from an established academic.
That being the case, your first step should be to try to get in touch with someone like that who can help you better evaluate your own work (and would, if appropriate, be able to suggest a journal). Probably it would be more effective for your teacher to approach someone, assuming they believe what you have done is publishable. (If you haven't gotten a teacher's opinion, you certainly should do that first.)