The backup will do all of your hard drive mate. You can't pick and choose.
Before you start, download the latest firmware on your computer and place it on a USB flash drive. You will need this to setup your new formatted HD. Firmware Download
Correct setup of the USB flash drive. Details here
. Flash Drive create a folder called PS3 inside that create a folder called UPDATE. Place the downloaded firmware inside UPDATE.
The second thing is to sync your trophies with PSN. Trophies are not backed up on the PS3.
Once that is done I would log out of PSN.
Connect the external HD to the PS3 and create the backup.
Depending on size this could take some time. Allow for a 200GB HD a period no less then 4 - 6hrs. If you can bare it I would delete anything you don't want backed up.
Demo games, game and movie trailers, etc.
The smaller the size the quicker the backup and restore later.
This video is pretty good at showing you how to remove the HD.
Video: Another look at PS3 Slim and its removable HDD
Just remember the screws can be a little tight but they will budge with enough applied pressure. Just don't slip otherwise you might strip the inside of the screws which would stop you from being able to remove them unless you drill the screws out.
Some written details on the subject of removing the HD on ehow
Remember take your time plan it out and nothing will go wrong.