Hello,
After puc you can opt for B.Com, B.Com LLB, BBA, CA . Apart from that, BMS is Bachelor's in Management Studies. It is more focussed on Analytics. Bachelors BBA+MBA Integrated programmes are in demand now. BBS is Bachelors of Business Studies is an alternative to BBA and BMS. BBE is Bachelor of Economic Studies and a 3 year Degree course more suited for Commerce students. BIBF is a 3 year course concentrating on International Business. Banking Industry has certain types within it like Retail Banking, Business Banking, Corporate Banking, Private Banking and Investment Banking. Each type caters to different entities. Retail Banking is what we engage with on a daily basis. There are National Banks and Private Banks. While National Banks start with career designations like Clerk and Probationary Officers, Private Banks call them as Tellers. For career in National Banks, you need to have atleast a Bachelor's degree. Any discipline would work. You need to appear for IBPS and if qualified, attend the remaining proceedings and if selected, you start at the ground level and based on the experience you put, you grow up the ladder. Private Banks might need a Commerce Background to be employed. A Bachelor's is mandate here too. But other types of Banking like Retail Banking, Investment Banking will require you to be a graduate in Finance or a CA. So you can start off with a Bachelor's degree and step into the Banking Industry or pursue CA and enter at a bigger level.

Hope this helps, Good luck.