The problem is, after a malware attack, there is no good way to be sure you're rid of it. At least not without doing a lot more work than a scratch and reinstall entails.
As for backing up beforehand, a good way is to burn a CD image of Linux, such as a recent release of Ubuntu or Knoppix. Then you can boot from the CD, mount the hard drive read-only, and copy off whatever you need.
Another way is to install the OS afresh into a different system folder or partition. Then boot that system and do your backup.
A third way is to remove the hard drive and install it into a healthy machine. Then use the healthy machine to browse extra drive and take off whatever.
A fourth way is target disk mode, in which your machine starts without booting its OS but, instead, via firmware, makes its disk drive mountable on another machine via Firewire or other high-speed interface. Macs have it. I don't know if any PCs do, however.
I agree with cynwoody.
Wipe it and start over. THere is nothing like a fresh intall of an OS. Then you can scan your files on at a time as you restore them.
After you have the system restored to a state that you would be happy to return to, I use Norton Ghost to create an image of the OS and the complete file system to a removable source that you can store away for retrieval.
Then all of this poking and probing for malware and whatever comes to screeching halt. Keep your work on a NAS. That, you can scan and clean without it corrupting your system again.
Get infected, insert the Ghost bootable media, wipe and restore and you’re done. Good as new. Your NAS files reappear at reconnection.