[Samsung Epic 4G Touch] Just_s:
Decent advice by patrao_n, but there are a couple of slight corrections.

With Titanium Backup, you can restore apps + data without issues in most cases, you just want to avoid restoring System Apps + data. Also, if you don't absolutely need the data, you will minimize the issues that some have - as noted by patrao_n - if you restore only apps.

As far as flashing a ROM, I would never advise a "one size fits all" solution (i.e before flashing a rom make sure to wipe everything like dalvik cache. cache. and also do the factory data wipe...) Instead, follow the instructions of the OP (original post) in the thread for the ROM you are flashing. The process can be quite different from ROM to ROM. Also there are three things that are your best friend before flashing, your two eyes and the search bar. Read and search thoroughly and you will find at least 50% and probably 90% of your answers on your own.

As far as your next questions:

Titanium restores app, data and some settings period. It is really nothing like a nandroid. It is meant to work in conjunction with a nandroid, but they are not the same. The nandroid is just like a restore point on a PC or a snapshot on Mac. The nandroid will take you back to the exact setup you had when you made it. Titanium will only restore your apps and some limited settings/data. External microSD and things like baseband (modem/radio) are not backed up/changed with a nandroid. You always want to have a nandroid (backup) of your preferred setup and I strongly advise that you keep a copy of that nandroid on your desktop (PC/Mac/Lin) as well. This way you are covered if something goes wrong.

AppBrain doesn't restore apps. It will tell you what you had installed and let you re-download them again one by one the same as the Market, but nothing other than a list is stored with AppBrain. It is basically just an alternative market.

In terms of restoring, there are any number of ways you can do this. Most third party launchers and many apps allow you to backup settings/setup to the sd. Using Titanium Backup Premium you can be setup in as little as 10 minutes depending on how many apps you have and how much you tweak your launcher. Also, whether or not you had to do a full wipe when changing ROMs or just cache and dalvik. Generally going from one version to the next of the same ROM, you are not doing a full wipe. Coming from one ROM to a different ROM you are doing a full wipe. Again check the OP of you particular ROM(s).

Personally, I use GO Launcher which allows me to restore my setup quickly and easily. Also I use the modified Format_All zip whenever possible so that all my data remains, meaning I don't really have to setup anything, just reboot and go. This doesn't always go as planned, but that's why you have a nandroid. More often than not it works for me. Typically I can change ROMs in less than 5 minutes using the modified Format_All.

Again, you are going to get much, much better advice if you read the OP and then ask questions in the ROM thread of your choice.

The one thing I can say, is take the time to learn. Don't take shortcuts before you know what you are doing or I can pretty much guarantee they won't end up being shortcuts.