hmm sounds like you’re on the right path. Especially coming from a poor high school your states seem ok. Just make sure your essays aren’t cliche and looks like you’ll have a good shot! good luck!!
Princeton has around a 5-6% admissions rate. A rate that low means that it’s going to come down to luck more than anything else. All the other schools on the list are roughly the same. You might get lucky enough to get into one of them…but you have to be able to pay for them too. Private schools vary widely how they disburse need-based aid.
Be sure you lock down at least one good full-ride scholarship. A scholarship is guaranteed in writing and you can ALWAYS count on it if all else fails.
Princeton would offer the best financial aid. Full ride (tuition and room-and-board) if your yearly gross family income is less than $65,000, and tuition-free for those with gross family income of less than $160,000. You have a good (higher than the 5% from 2019) chance. Good luck.