When you create the backup, that backs up your email account settings as well. It doesn't save the email messages themselves, but it saves the account settings. Your contacts, notes, Safari Bookmarks, Safari History, app data and app settings .... And more are contained in the backup.
When you sync your iPad, that should transfer all of your apps into iTunes on your computer. That in essence is how your apps are "backed up". They are saved in the iTunes library on your computer. So no you do not need a list of your apps. You can find that list in your iTunes account.
So.... Backup, transfer purchases and the sync your iPad and all of you app data and device settings will be in the backup, and all of your iTunes purchased content will be in your iTunes library. You will be good to go.
Connect the iPad to your computer with the cable and launch iTunes (if it doesn't start up on its own). If the iPad syncs automatically, so much the better because it should backup and transfer the purchase into iTunes. But just to be safe, after the sync completes - while the iPad is still connected to your computer and with iTunes still running, right click on your iPad under the Devices heading and select - Backup. Let the process complete. Then right click on the iPad under the devices heading again and this time select - Transfer Purchases. Let the process complete. Sync the iPad one more time and then you can eject the device.
You will now have a current backup - and all of your iPad purchase content will be in iTunes on your computer.
Are you really still running iOS 3.1.2? Do you want to update the iPad and is this why you want to backup everything? It's a good idea to backup no matter what, but I'm curious as to where all of this is headed.
You can read this to see what is contained in the iTunes backup.
http://support.apple.com/kb/HT4946