The first thing to remember when trying to programmatically interact with a banking website without express written permission from the bank will MOST LIKELY be a violation of the website use agreement, and may land you in more trouble than it's worth.
Second, you DON'T want to start 'learning' programming by trying to tackle something that massive and sensitive. Not that there is anything wrong with the eventual goal, but that's a journey of a thousand leagues and you need to take your first step.
I would say start with a simple programming environment, like python, or perl. Reason, you don't have to worry about linking, libraries, code generation etc. Get used to the basics of what you want to achieve functionally, them reimplementing that in C++ or Java would be the next step.
To begin with focus on learning client-server programming.
Write a client, write a server, learn all about sockets, learn all about TCP programming,
then learning about secure socket layers (SSL) and transport layer security (TLS).
Once you've done this, try switching to C++ or Java and see if you can repeat the effect.
There are TONS of tutorials on these topics.
Once you have become used to that, learn what tools and libraries are already available to do most common things. For example libcurl is great for creating common internet application protocol clients (HTTP, HTTPS, FTP and the like).
See if you can create an interactive program that you can "log in to" using your web browser which outputs stuff in XML and formats it using cascading style sheets.
This should lead you into javascript world, where there are powerful tools such as jquery. If you mix and match these correctly, you will find that development can be a LOT of fun and quite rapid.
:-)
Happy journeying.