Economics or Finance are the most logical choices. Lots of math people,too
In addition- you need to like working in teams. Part of your job responsibilities will include making sure that you follow procedures when opening accounts, conducting wires transfers, cash handling, ets. Making sure that you in compliance is the number one priority because the banks want to make sure all your daily paper work is in compliance either wise the banks and our branch will get fines and you will be coached around your operational excellence performance,range. So, being a banker- you will be held accountable around sales, service, operations and your company values and mission statements .
It depends whether you want to be in commercial banking or investment banking. Commercial banking caters to your everyday customer operations, this could be Northern Trust, Chase, Wells Fargo, etc. The investment banking sector caters to companies that are trying to make larger investments. Both are considered banking but are very difference fields to step into.
Withing banking industry your have a wide variety of roles that you can go, from IT, software development, economics, finance, accounting, risk management, audit, commercial, marketing, etc... it is going to depend on your preference and how do you want to focus your career.
So, if you mean purely the financial services industry, finance, accounting and audit are great options for you.