I just changed the oil in my 2001 Hyundai Tiburon today. I know it's not the same year as yours, but I put 4 quarts in mine. I checked the stick under the hood and it showed that it was about full.
A 2001 HYUNDAI TIBURON WILL TAKE APPROX. 3.7L
5 quarts
as far as 2002-2004 it has 185 stock hp
it should take 4.7 quarts with oil filter
$800 give or take
The answer is use 10W-30 for engine oil in the 2003 Hyundai Tiburon GT.
The 2004 Hyundai Tiburon OBD 2 port is behind fuse box door, left above hood release
on the bottom of the oil pan
5w-30
10W-30
10-30w