You should be fine for HYS. Typically people recommend applying early for primarily scholarships as there is a larger pool of $$$ in the fall. But in the case of HYS, they only do financial aid so you applying in January will be fine. Good luck!
Thanks, @alexandergreene93! It sure is a lot to think about, to say the least. He has an interview tomorrow for an MIT position, and so he says that I can go to Harvard (to which I roll my eyes and say "yeah, once I get a 180 on the LSAT...")! :)
Stanford, Harvard, Chicago (Booth) and Penn (Wharton) are king. The most elite investment banks and private equity firms to refer these schools to others, as they are the best of the best.