I made a little typo on the title (Does this paragraph read well?)

Hello! I just want to hear your comments on the style of the paragraph. Thanks!

College applicants don't just choose their schools based on academic reputation and excellence. Financial consideration is perhaps the biggest factor in picking the right school, especially when one avoids serious debts. Sometimes, this factor leaves students no other choice but to enroll in a lower-tier and non-ranking school. But this shouldn't discourage them from pursuing graduate studies, even when statistics show that most prestigious universities prefer applicants from an Ivy League school.

Just not true though - countless students apply to schools with scholarships. Even Harvard has more than half their students on scholarships. And your last sentence isn't one bit true - sorry.
In the US, graduate school is after 4 years of undergraduate college. I have a feeling it means something different where you are, because you are mixing 'college' and 'graduate school.'
To my mind, the biggest factor in applying to college is how well the student did in high school!
The biggest factor in applying to grad school is the concentration of studies in an area the grad school is noted for, the interview, and the thesis.

I have a problem with this statement: even when statistics show that most prestigious universities prefer applicants from an Ivy League school.

Are you talking about bachelor students opting for their Masters? If so, it needs clarification. Even so, I wouldn't agree with that AT ALL.