The type of student who should attend BYU-Provo is someone who works hard and has incredibly high moral standards. BYU students pride themselves on being friecely competitive for scholarships, grades, etc. There's an atmosphere of success and BYU pride all over campus, and you can't escape it--you might as well want to join it. Since BYU is a private school owned by the LDS, it expects every student to sign and live by the Honor Code, which describes moral standards which some find annoying; however, these standards actually work to create an atmosphere of cleanliness and respect. Honor Code includes things like avooding drug and alcohol use, wearing modest dress, being clean shaven, refraining from sex until marriage, etc. if you don't want to live by this code, then you shouldn't come to BYU. This code serves to keep the campus and its students comfortable.
The type of student who comes to BYU Is one who wants to push themselves spiritually (even if not a member of the church), physically, and mentally.
Oh, and they want a great education for a cheap price (LDS students pay less because they pay tithing, but but the church subsidizes the education go all students who attend BYU).