BBA

You may refer to following link for list of top BBA colleges in India: https://www.shiksha.com/bba/ranking/top-bba-colleges-in-india/93-2-0-0-0.
You can do BBA at VIT University. It is a good university.

BBA will give you basic understanding and exposure on different management functions which can help you to run your own business. You may get supervisory level jobs after BBA. You will have to do MBA for better career growth.

If you want to do MBA after BBA then CS is not necessary. You can do MBA after BBA. But if you have interest in CS then go for it, gain some work experience (1-2 year)n and then go for it, so that it would be better for your admission and placement in an MBA college.
Provided you do MBA from a good c

You can refer the below link for college comparison: https://www.shiksha.com/resources/college-comparison-90734-228748

NIMAS | Barrackpore, Kolkata
Prajnanananda Institute Of Technology and Management | Park Street, Kolkata
Carreograph Institute of Management Studies | Shyambazar, Kolkata
Dinabandhu Andrews Institute of Technology and Management
Eminent College of Management and Technology | Barasat, Kolkata
Nopany Inst

IIPM (Indian Institute of Planning and Management) closed all its 18 campuses across the nation in October 2015. The institute made this announcement on its official website.