Please don't top-post. Message rearranged for easier reading
comprehension.
You misspelled "used car" there. New Hyundais are cheap, but a 1996
Toyota Corolla is cheaper, even if it needs $1000 worth of work. You
might want to post your geographical area. NYC != LA != Ann Arbor !=
BFE, and differing conditions in differing areas may mean one model of
Hyundai will work better than another.
On the basis of good experience with my 2003 Elantra GT, when my 16
year old needed transportation last November, I got her a 2002 Accent.
So far, no problems and she loves it.
YMMV on that Accent. My mother rented one when she spent several weeks
in California last year, and she hated it. "Tiny, didn't accelerate
very fast, felt like it was going to fall apart any second" was how she
summed it up. FWIW, I have a 2003 Tiburon GT, have never had any
mechanical trouble with it, and love it. (You do *not* want to give a
16-year-old a Tiburon GT, though. If I'd had my Tib when I was 16, I
would've wrapped it around a tree in less than a month.)
Make sure you tell your daughter about regular maintenance, and make her
buy her own gas and pay for oil changes/whatever (or teach her how to
change the oil herself, if she wants to learn.) Taking care of a car
takes some time and money, and the sooner she learns that, the fewer
problems she'll have later on.