Thank you for the question. The K-1 fiance visa is generally a much better option than a student visa if a person is eligible for both visas because it is more direct way for your fiance to obtain lawful permanent residence in the United States.
The process is outlined briefly below:
Step 1) After you become a US citizen, you would file the 129-F with USCIS. USCIS.gov and click forms.
Step 2) After the petition is approved, your fiance would fill out the forms sent to him by the National Visa Center.
Step 3) Your fiance would be interviewed at the nearest US consulate
Step 4) Your fiance would enter the US.
Key Points to remember would be that you and your fiance would need to be married within 90 days of his arrival to the US and he would need to adjust status to a lawful permanent resident within those 90 days using Form I-485
or be required to return to her home country.
The eligibility criteria is fairly simple:
a) U.S. citizen spouse
b) Both parties are free to marry
c)genuine intent to marry upon arrival to the US
d)both parties must have met and seen each other in person within the
last two years.