CBSE 12th

Hello,
After completing class 12th, I would suggest you to appear for IIT JEE and AIEEE. These two entrance examinations provide admissions to IITs/ NITs and other government colleges, which are cost-effective.
I would also suggest you to appear for individual state examinations (OJEE in Odisha, EAMCET in Andhra Pradesh/ Telangana, COMEDK in Karnataka, etc.). These exams also guarantee you good colleges and serve as a backup in case things don't end up the way you've planned for IIT/ AIEEE.
Every state has its own share of good engineering colleges. So, don't underestimate or overlook them. They can prove to be vital. The more the entrance examinations you appear for, the more the options you will have for choosing colleges.
Certain private colleges like SRM, KIIT - Odisha, GITAM Vishakhapatnam and ITER - Odisha conduct their own entrance examinations. You can opt for these as well.
After the results of those entrance examinations are announced, if you have a valid score and rank, you can attend the counselling procedure for the respective entrance examination. During the counselling procedure, you can select a college of your choice and the branch of engineering.
I hope it helps. If so, kindly, upvote this answer. If you've any further questions, kindly revert.

In Science, you have engineering and medical. These are the traditional streams students choose. Some new streams are also in demand nowadays like bio- tech, nano technology, agriculture and genetic.
Students are also moving in fashion designing and interior designing. Research oriented students can go for KVPY and get into institutes like IISC or IISERs.
There are courses like mechanical / electrical and computer science in engineering to newer ones like hotel management and fashion designing. You can opt for any of these as per your interest.
I hope it helps. If so, kindly upvote this answer. If you have any further questions, kindly revert.