B.Com

b.com honors is much better than simple b.com

You can appear for B.Com or BA via the open university or correspondence route .The duration could vary from 1 to 2 years

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.