For what it's worth, I only applied to one university (not quite Ivy, but real close), and I graduated in the top 1% of my high school class with a near perfect GPA. I had no doubt I would be accepted really, so I wasn't worried. However, I applied via their Early Decision program. If I didn't get accepted via Early Decision, there would still have been time to apply elsewhere. Not that there really were any other schools on my radar. Anyway, if Brown is your first choice by a wide margin, you might want to consider Early Decision, assuming Brown has something like that. The best part about Early Decision is that you find out in December and the stress is gone (if you've been accepted, of course). Meanwhile, all your peers are still stressing out until like March or whenever colleges normally send out their acceptance letters.
Not that anyone cares, but something like 80% of my tuition was paid by a combination of performance-based (i.e., scholarship grants) and need-based financial aid. I paid about 15% in student loans (which took me like 4 years to pay off). My parents paid about 5%. If you have rich parents though, I guess you can forget about any need-based financial aid...
