B.A

In India, many institutions do not know the difference between Game Art, Game Design, Game Programming and Game Scripting. Except one or two premium colleges, the others have got a very weak curriculum which is a mixture of game art, game design and game programming. Or merely game art course which is misinformed as game design course. The B.Sc, BA, BFA do not matter at all. Depending on which university has given the validation, the courses are named as B.Sc BA or BFA. If we go as per international colleges, a game design course is always Arts oriented so it must be called as BA only. But in India, parents and even students wrongly assume BA as useless and only fit for nothing students would study BA. Certain fine arts universities have started giving approvals to colleges to conduct game courses. Such names will be BFA only. Look out for colleges which offer Dual Degree in Game Design wherein you have the advantage of both Indian and International Degree at the same time. Also, go through the detailed content and curriculum. Suppose, you are unable to understand the value of a content then consult any expert in the field of game who will be able to tell you which college offers the best course content. Also, check whether you are fit for a game design course. You need to be very good in logical reasoning, you should have good communication skills, you should be keen to learn fast changing technology, you should be able to generate new and interesting ideas which would make a good game. Many in India wrongly think that if they have good art skills, they can become good game designers. That's wrong. If someone is good in art then they should join game art course and not game design course.

It will be difficult to get a good job just doing BA.Arts. There are many specialised courses available after graduation as Diplomas or Master's degree.
As I am not aware of your interest areas, but still trying to give some options as:
Masters of Business Administration (MBA): The most potential career option after graduation in Arts is a degree in Management or Masters of Business Administration. The 2-year management course from a reputed institute paves the path for a career in the field of business management. Some of the reputed entrance tests conducted by the best institutes are CAT/MAT/ XAT/ FMS/IIFT/SNAP.
Masters of Arts (MA): Going for a MA degree from a reputed institute can open the doors for M-Phil and a PhD program, which further enhances the job opportunities, especially in academics and research.
Popular Professional Courses
Hotel Management: Demand for trained professionals in the hotel industry has been constantly growing.
Travel and Tourism: Tourism industry is another sector which has bright job prospects.
Fashion and Textile Designing.
Journalism and Mass communication.
B.Ed
and many many more.