Which have the student and teacher meeting before the first class, like each other or at least have a substantial interaction before they get into the drama.

A good example is Hello Mr. Right. You know, something where they're into each other without it being creepy and has a happy ending. 

Preferably Korean or other dramas, not so much J-Dramas since I struggle to get myself into them and the guy is almost always a cold jerk.

Hmm, maybe Flower Boy Raymun Shop, but she doesn't stay as a teacher during the entire series. 
Also, try Biscuit Teacher and Star Candy. I'm a bit hesistant to rec it cos I can't quite remember if they meet before she becomes his teacher, but from the parts that I watched, it's pretty sweet and funny. 
Korean drama Doctors...http://mydramalist.com/16192-doctors

I kinda liked it...the main guy isn't a jerk :)
Only problem is that the plot is kinda weak. Some people find the story a bit boring and draggy...but I didn't feel the same.
There aren't major love triangles though....most of the time the main female lead and main male lead are in peace!
Thumping Spike, female lead is young volley ball player who ends up having to coach a highschool volleyball team and male lead is student who falls for her.
Also try Drama film Nara's Rain it on kbs youtube main channel for drama specials. Female lead teaches at a highschool but has a forgotten past connection with male student in her class, they have an innocent friendship but people start questioning them about it.
Sand Doo Let's Go To School but in it the main characters are the same age (used to be classmates)
Kou Kou Kyoushi
Thanks for the suggestions guys, I'll put them on my PTW list! Anyone else have anymore?

IzzyDramaLover- I watched Doctors after being on the fence for months! Binged it all day and LOVED IT! Thanks!
Majo no Jouken (drama): they only meet briefly before being teacher-student.
Close Range Love (movie): I don't remember anymore, but I think they don't meet before being teacher-student.

I second whoever said Biscuit Teacher and Star Candy. That's my absolute favourite teacher-student drama.