BITS is pretty affordable.Its about 30% costlier than the IITs . Look , if your parents income is like below 3 lpa , you'll get a 50% off just for being above avg CGPA!! I'd insist you try to pitch for some funds and try for BITS too.I assure you its worth it.
Apart from BITS you might want to go for DCE.Your rank is great , you'll get something good at NSIT.