Wow, you have got a few bumps to get over before you will be able implement anything close to what you are talking about doing.
You'll find some helpful info here:
http://www.pdfscripting.com/public/department48.cfm
The first thing you need is some perspective. LiveCycle Designer is a tool for creating a special type of PDF form, called an XFA form (or XML form). Both Acrobat and Adobe Reader know how to interact with XFA forms. So the user's only needs Acrobat or Reader, they do not need LiveCycle to use these forms. LiveCycle is only a design tool for creating the form.
XFA forms are a relatively new technology. There is also a traditional AcroForm model. To create an AcroForm you add form fields to a regular PDF using Acrobat Pro or Standard. So you have two forms technologies AcroForm and XFA. You create AcroForms in Acrobat and XFA forms in LiveCycle. But both form types are displayed and used in Acrobat and Reader.
The only forms technology that can talk directly to a DB is XFA. If you want to create XFA forms you will need to learn about XFA form design and the XFA Scripting model. However, XFA forms will only connect to a local DB from Acrobat, not Reader. By local, I mean a DB on the user's file system. Possible a shared drive. It is possible to connect the form to a remote DB, but the user will need to have the correct DB drivers installed on thier own system. This DB connection will not work (or work reliably) for random users on the internet. Also, it only works for users on Windows. A Mac user will not be able to use a DB connected form.
The only way to reliably connect the form to a remote DB, for any user, on Windows or Mac, and from Reader or Acrobat, is through a server script that handles the data transactions. Your project is not impossible, it's just a steep uphill climb.