I'm thinking, if I want to do a complete wipe and also format the SD card to get rid of a bunch of old crap, what do I need to extract from the phone and then put back in for TitaniumBackup to still work? Is there a single folder that contains all of TB's settings and backups that you can just copy and then put back in to restore apps and system settings? Or does TB stash settings/backups in several places on the SD card?
All you need is the TitaniumBackup folder on the SD card. This contains all your backup information.
Make sure to have the
Auto-sync TB settings preference checked. Titanium Backup, ironically, won't back itself up when running a backup. This check-box ensures that your settings for the app are saved as well (such as schedules and preferences).
You can also create an update.zip file which can be used to install TB in the recovery: Go to the menu, click More, then scroll down until you see
Create "update.zip". This particular file will not be stored in the TitaniumBackup folder, but rather on the root of your sd card.
After you wipe everything, just copy the TitaniumBackup folder back onto the SD card, install your rom, and install TB (either from Google Play or from the update.zip file if you created it). It should automatically pick up all its old settings and be ready to restore your apps.