Make sure you can see your email in the Gmail app. If you can't, then your Google account isn't properly set up. You can also go into All Settings, General tab, Accounts and Sync, and it would be under Google, and then under Accounts, under which should be a lot, including an entry for Contacts, make sure it's checked, and try unchecking and rechecking it to force a re-sync.
You can't switch a contact that's already been created. To choose where to store a new contact when creating it, tap "AT&T Address book" up near the top, just below "New Contact." That should show you your other options, such as Phone, SIM, Google, etc, depending on what you have available.
Maybe it would help if you could post a screenshot of what you're seeing, using the QuickMemo function.