B.Com

There are ample amount of courses which you can pursue after 12th other than BBA and B.Com. Some of the courses are Architecture, Bioinformatics, Forensic sciences, Biotechnology, Interior designing, Pharmaceutical- B.pharm, Engineering, Hotel Management, Fashion Designing and many more. I can suggest you some top ranked universities like Delhi University, JNU, Lovely Professional University, Banaras Hindu University etc. you can browse website of these universities to know more details related to the course.

The name of program will not be hons. You need to get a good IELTS or TOEFL score and apply by Jan for September intake. Write a strong statement of purpose and have a list of extra curricular activities to report to

Delhi Faculty Of Management Studies (FMS) Indian Institute of Management Kozhikode (IIM-K)
Indian Institute of Management Indore (IIM-I)
Of course you can always pursue that.

Yes, Private college is a good option for you in your degree because it offers students training and campus recruitment and also B.com is a good course which offers you a good carreer opportunities in business field!!

PGDM stands for Post Graduate Diploma in Management and MBA stands for Masters in management. IIMs don't have MBA, they have PGDM. So, Its all depends upon the college or university you are choosing. Like if you are pursuing your MBA from LPU or Amity, the value of that course isn't good as compare to PGDM from IIMs. You better check for the best b-schools in the world or india. This game is all about the ranking. If you get admission in best college or university don't look for MBA or PGDM just do what you get.
And don't forget to give entrance exams like CAT, MAT, CMAT, GMAT etc.
Best of luck for your future.

Many courses are there like CA-CS foundations, M.com,MBA after graduation .