I think you have things grouped up a little too much. Gingerbread is Android 2.3. Pretty much the latest Android OS for phones right now. Prior to that Froyo 2.2 and before that was 2.1, 2.0, 1.5.....
Liberty and ApeX along with others are modified versions of the various Android platforms and referred to as ROMs. All of the ROMs require root status to install.
Each ROM has been tweeked buy its creator to improve performance, add features and in some cases take away features such as Blur elements which tend to slow down the phones performance. Be aware that each ROM requires a particular Android OS and they are not interchangeable.
Before messing around with ROMs, you need to understand the SBF process to return your phone to OEM status as well as how to back things up. I personally no longer make backups, I just wipe it all clean and install whatever im installing fresh. But my phone is just a toy and not a business or social interface so I dont stand to loose much this way.
The latest batch of ROMs are for GB leaks. There have been 3-4 leaked versions of GB in the past month or so and each one seems just enough different that you need to be on your toes and read and follow the install directions carefully.