Hello,You can reappear for PUC exams. The best option for you is to appear for regular examination of 2nd PUC.
There is no advantage of reappearing for supplementary exam. You can appear for regular exam with same registration number. You need to have your documents of first year of PUC to apply for exam.
Other than that 2-3 photographs, identity proof of high school and required examination fee. Stay updated with  official website ( http://pue.kar.nic.in/ ) for more info and latest updates !!!

ALL the best