Technology i should use
Online Banking: You are basically asking people to entrust there credit card details to you. So you should use PHP, HTTPS, MySQL, Some form of encryption etc... etc... basically what you need to do is learn PHP, Apache and MySQL, Next you need to actually buy a server. they cost $300/month with ISP: http://www.hostgator.com/windows-dedicated-servers.shtml
Now don't go thinking that you should just build your own server, they are a bitch to set up and this is frankly cheap if you include certification. HTTPS is your certification. without HTTPS you are not telling your server to encrypt anything, your MySQL databases would require encryption and frankly from the fact that you don't know any of this if i were you, i would not even try starting until you have a good grasp on this. However if you do want to just do a quick and easy route, then get a merchant account with paypal and use them for your HTTPS, that means no server (no $300/month costs) and is much MUCH easier. Use paypal as your idea makes you liable to lawsuits if you do get hacked/you f**k up.