Clean Install of Lion OS X / Optimizing My Machine
The best way to back up your documents is to back up your entire hard drive (aka "clone").

I use SuperDuper for this (you can use it for free, although the SmartUpdate feature is worth paying for, IMO. CarbonCopyCloner is another program which many people like).

Once you have a bootable backup of your hard drive (verify this by actually booting from it!) you can make a clean installation of your computer. From there you should be able to use "Migration Assistant" (/Applications/Utilities) to copy files and applications from either Time Machine or your clone.

Ok, now, having answered the question that you asked, two comments:


10gb free isn't a whole lot of space, especially if you are on a non-SSD drive.
If you are having problems with your current installation, I would highly recommend that you do not use Migration Assistant or any other method to automatically copy files from your current setup to your new one.


Instead, I would recommend that you keep the clone handy, and if/when you need files from it, then copy them. If you need an app, go make sure that you are downloading the latest version from the website, and install that version.

Most applications will run from the backup drive (some which use installers might not) so if you need quick access to some program, you can probably just run it from there in an emergency.

You can get a 500GB bus-powered USB drive for about $50 from Amazon [note: I just picked that one at random, it's not a specific recommendation] which will fit easily into your laptop bag.