no the fees structure wont change according to the rank. You will have to score such rank in the desired college you like to enter in the state of karnataka. so for less fee structure you need to score a higher rank in order to get selected in the desired college you need to.
and as per the best course in engineering, every field is best in its way....but in todays world IT sector is getting a bit faster and enhanced. so if you want  to settle easily Computer Science or IT is a good option for your career. thank you and all the best!!