In my country the online payments are not an old thing, the first time i saw a web application taking payments directly to a local bank account was last year.
So, Im
At miniumum follow the PA DSS (Payment Appliction Data Security Standard). More info can be found here:
https://www.pcisecuritystandards.org/security_standards/pa_dss.shtml
Also it would be wise to look at PCI DSS, which could be found here:
https://www.pcisecuritystandards.org/security_standards/pci_dss.shtml