If there is a university close enough for you to live at home, and if you get a scholarship or other financial aid that covers 100% of tuition and fees, then you might be able to pull this off with very little debt. Otherwise finances are likely to be a significant issue.
I do not know all that much about Purdue, other than it is well known and very good for various types of engineering and CS. I expect that it is also likely to be very good for neuroscience if you get accepted and if you can afford it. To me your stats look pretty close to the average for incoming students at Purdue, and you are in-state, and it has roughly a 50% acceptance rate. To me your chances there look pretty good, but I do not think that I would call it a safety.
Which to me raises the issue of what will happen if you do not get accepted to Purdue.
I think that you should submit your SAT score to Purdue. On their web site I see ‘Purdue University is "Test Expected,"’. Also, your SAT score at least according to Prepscholar is slightly higher than the average for incoming students.
Are any of these schools close enough to home that you could live at home and attend? If so, then I think that you should very seriously consider sending in an application. I also agree with others that you should take a very close look at in-state options and see if any more of them (other than Purdue) have an acceptable program in your intended major. You do not want to be in the situation that you have no affordable options.
One daughter had a friend who was in a financial situation similar to yours, with divorced parents and living with a parent who could not afford to pay much if anything (some details were slightly different). She was like you a strong student. She attended community college for two years, did VERY well, and then got accepted to an in-state public university with a full tuition scholarship. She was able to live with her father the entire time (a good guy who I knew quite well from school events). I happened to meet her in a store near my home one month before she graduated university with a marketable major and very little debt. She had a big grin on her face and was doing very well. You might need to take a similarly affordable path to getting a bachelor’s degree.
Some of your out of state options are a reach for admissions (eg, Amherst College, Vassar College). Some are a reach for affordability (maybe all of them). I think that you should make sure that you will have an affordable option, although I suppose that starting at community college is an affordable option and I don’t know if it would need an application this early in the time scale.
Do you have an intended or likely career idea with a bachelor’s degree in neuroscience?
Neuroscience is a major where some form of graduate school is likely. A PhD is typically fully funded (with a stipend which is sort of just barely enough to fully live on). However admissions to PhD programs is very, very competitive (a high university GPA, good research experience, and good references are important – you can get this at any of a very wide variety of universities). Other forms of graduate programs (eg, master’s degree, MD) are typically not funded, and can be expensive.
Minimizing debt for your bachelor’s degree is important.
With your being nearly in the top 10% in your high school plus a top 10% SAT score and an intended STEM major a person might hope that this would be straightforward, but it isn’t. Best wishes.