I'm paranoid so I use several at once. Time Machine is a good place to start. It's basically set it up and forget it -- it works in the background and gives you versioning as well (if you change a file you can go back to an older version). Since you will have a portable computer the easiest way to go about this is to buy a TimeCapsule so the backups are wireless.
Using TimeMachine by plugging in an external drive (on a portable system) is a pain and an easily "forgotten" task.
I'd also strongly recommend an off-site backup to take care of loss by theft, fire, or natural disaster. A "cloud" service is the easiest way to go here. I use CrashPlan. The third backup method I use is disk cloning which isn't as effortless as the others, but with a cloned drive you can boot from it and be up and running after a disk drive failure basically instantly.
I have to disagree with an earlier post saying to buy a Thunderbolt or USB 3 drive for this (although USB 3 drives don't have much of a premium). A speedy drive isn't really needed for backups. Four systems here are backed up using TimeMachine to a drive on my server system. It's USB2 and works fine. Since the backups are incremental (even the cloned drives) rather than copying everything with each backup, not much data needs to be moved. Typically more time is spent determining what needs to be moved than actually moving the small amount of data!
