OP: No need for community college, what about University of Florida? With those scores, you will be eligible for Bright Futures FAS, which should take care of tuition. Room and board might be tougher, but Gainesville is cheap to live (at least compared to NYC and Boston!).
For the SAT, look at the Meltzer books (grammar and reading strategy) and read, read, read as much as you possibly can. Take the Math Level 2 test, because the curve is much easier than Level 1. I have known personally a number of first generation and poor kids from poor schools who got 1500+ on the SAT, and that was back in the 1980s (1500+ back then would be equivalent to 1570-1600 today). Don’t give yourself an excuse because of your humble circumstances. Put your head down and do the best you can, on the tests and on your applications generally. Good luck!