What is the best way to get the girl I met online to the US?

She can try to apply for a student visa but for that she first has to be admitted into a school/college/university/program that will provide her with the necessary documentation to apply for the student visa at the US Embassy in Lima, Peru. There is no guarantee that it will be granted if she doesn't have sufficient ties to Peru that can be documented and is believe to have possible immigrant intent. A fiance visa is certainly possible as well if you are really committed to marriage. This process takes about 9-12 months from start to visa issuance. Then she would get the fiance visa for entry to the US for 90 days during which time she has to get married to you and then file for adjustment of status to permanent residence on the basis of marriage. For those who are seriously committed, this is a good path; however, if you just want to see how things go, it may not be the ideal option for you.

A student visa is more difficult than a tourist visa. So her chances of getting it are really slim. You can do a fiance visa. That should work about 98% of the time as long as you can prove the relationship. It takes almost a year for that visa, however.

If a visitor visa gets denied multiple times, the same is likely for the F-1. If you meet in-person, like in Peru, you could then sponsor her for a fiance visa, but generally, you must have met in-person first.