I highly recommend using TrueCrypt because it is a free and open-source solution that provides on-the-fly encryption of the entire hard drive (or a specific partition, or a file that can be used as a fully mountable partition).
TrueCrypt (free and open source)
For your convenience, I also located a web page that provides some instructions for installing and using TrueCrypt on Ubuntu Linux (the Operating System that you indicated is of interest to you):
How to: TrueCrypt setup on Ubuntu Linux
The fact that you want to run backups is excellent, and I strongly encourage you to do this regularly even after you've finished encrypting your hard drive (your question deserves an extra point in my opinion for mentioning backups).
In my experience, TrueCrypt (which beats the pants off the commercial-grade competitors I've seen) has proven to be 100% reliable for all my clients who are using it, and for my laptop -- it doesn't seem to matter that the power is lost or there is the occasional unexpected crash (mostly encountered with Windows), the system carries on where it left off, and disk repair options appear just like they do on unencrypted systems. In my professional estimation, it appears that the TrueCrypt developers "got it right," and I trust this product for reliability and security.