Lots of security concerns here. Even if you aren't subject to regulatory statutes (depends on your business) I can think of quite a few. I'll type till I'm tired of it.
- Are your servers secure? Locked in cages, secure site, two-person access, patched, audited and scanned with intrusion detection, and so on. This is the most likely thing you've got to worry about. If you think they are, they're probably not.
- Is the network secure all the way down? Even stupid things like a plan to make sure your domain name doesn't expire is important. Do you have automated controls for shutting down the site in case of intrusion?
- Is your software secure? Auditing by a third party for security problems is a must. Don't skimp on this. From the front end (CSS attacks) to the back end, everything needs to be locked solid.
- Is your development cycle secure? Dual-person controls on the software. Don't let your developers patch the servers, or deploy code without a code review. Admins need monitoring too.
- Everything needs to be encrypted. Better to not store the account numbers at all. If you do store them, encrypt them and keep the keys elsewhere.
... okay, I'm tired.
Not to rain on this parade, but if you have to ask about this kind of thing on SO, you're really not prepared to do this. Buy a solution, hire a professional in the field, or spend a lot of time studying this problem and have someone audit what you're doing.