Welcome aboard kateb, there's no "easy" answer. The first place to look is to read up on the security measures in respect to storing credit card information and PCI compliance. Although it's specific to CC info, this will give you an idea of the gravity and liabilities your client is in for.
how do I ensure the information stored on each client page remains secure and no one manages to hack in and steal their information?
The only honest answer: you don't. Anything can be hacked. You can decrease the odds by having a dedicated server in a location under your control (i.e., shared or commercial hosting is out of the question) and there are limited services that offer certified security of their servers. And it's expensive.
There are so many aspects to this it's not just your scripts, it's the security of the server it's on, the network on which it resides, the physical security of the device, the security of all those accessing it . . it goes on. Additionally if you're in the U.S., the new Red Flags ruling is going to make things even more dicey, everyone seems to be ignoring it right now but it's a reality.
Now, I know of clients who are, to this day, accepting sensitive information via email, storing credit card info on their servers, and have done so for years, claiming "I've never had a problem." Good for them, but it only takes one mistake and they will be in a very big pile of trouble. You can drive for 20 years withou car insurance until you injure someone . . . then everything changes.
Start by looking at the policies for credit cards, this.
