What to expect as a student from a low income school that has never had anyone go to the Ivy League?

Answered

While my school was about 20 minutes away from Penn and usually got 1-2 students in there each year, it was pretty similar to the other things you're mentioning (low income, low average scores, majority on free/reduced lunch, one counselor for hundreds of students, "rough" reputation, but offering a lot of AP and college level courses), so figuratively speaking I know where you're coming from. It's by no means impossible to get into an Ivy (or something similar) from that kind of school, but the reality is that you will have to work harder than people in a lot of other schools, especially wealthier ones. Both because you may not have the same opportunities afforded to students at schools that act as "feeders" for Ivies and because you'll have to do most of the legwork yourself, because your counselors may not be able to help you in the ways that more connected ones do. I still distinctly remember getting to know people at my college for the first time, hearing about their high school experiences, and realizing just how much easier it had been for them to reach the same place.

First things first for that, you'll have to make sure that you're proactive in getting together things like your teacher recommendations, counselor recommendation, and transcripts. If your counselors are seeing 600 students apiece, you might need to set up a cadence of meeting with them individually whenever you can to build a rapport. Just make sure they know you so that they can effectively submit their recommendation, which is important for putting you in context with the other people at your school.

Beyond that, take as rigorous a schedule as you can manage, because whatever the opportunities at your school are like, colleges want to see you taking advantage of them. Same goes for extracurriculars—do what is available to you, and whatever is connected to the things you want to study. Aim to have some leadership if you can, and if there's not much you can do at your school, look for things to do outside of it. Across all of that, try to build up and demonstrate some kind of cohesive interest or passion; it could literally be anything, as long as you're able to show that you can commit to an area of interest and develop it independently through the classes you take and the things you do in your free time. And do test prep—strong test scores, if you can manage them, will make sure you can get your foot in the door for these schools.

Finally—apply to a bunch. It will take a lot of time and effort, but all of these schools are so hard to get into that anyone applying to them really needs to apply to several for the best possible shot. Pick the ones you like (whether that's Ivies or other similar schools like Stanford, Rice, Duke, Vanderbilt, etc.), and apply to as many as you have time for. If you're in Florida, you have basically the best target option imaginable in the University of Florida, which is an incredibly good and incredibly inexpensive public school for FL residents, as well as good safeties in the other Florida state system schools, so you're in a good position to dedicate most of your time to reach schools.

Hope this all helps—let me know if you have any questions.