I can only speak as a young person, not a female. :-)
I had a successful FUE surgery at 25. The place most of the focus was on.. front hair line
FUE - Is the only way to go, forget the KO response. lol It's safer, no scar, fast heal time. And because you don't have too much to focus on it won't be the most costly. I'd just say confirm with many Doctors if you're age is okay to have the procedure done because I recall overhearing it's best to wait until maybe 23.. But feel free to do your research.
Keep us posted!