Mac: back up to cloud storage or iPod I need to hand back my current MacBook Pro, and setup up a new one. What I want is to save my all user-specific data and, maybe, all the programs installed (not necessary).

I believe it is possible, having an external HDD, setup a Time Machine to back up all my system to it. Yet I see this to be not the best solution: I don't have much time left with my current MacBook + I would like to lower my expenses as much as possible, solving this problem.

So my question is: is it possible to order, for instance, a non-expensive external dropbox-like storage and setup of Time Machine to use it? MIf not... I have a 80 Gb iPod Classic – are there any known cases of backing up the system to IPods?
If you can have both machines for a period of time you can use Migration Assistant to copy your user directory directly from one Mac to the other.

While an iPod can be used as an external disk practically speaking it's an expensive and somewhat delicate mechanism for doing so – iPods get very warm when used as data drives for extended periods. External hard disks are (by most metrics) cheap these days, and will generally be more reliable than the micro hard drive in the iPod.   My first choice for backing up to an external drive is SuperDuper!

I don't know your definition of expensive but for offsite "cloud" storage, I recommend CrashPlan. You can pay for their cloud storage–50 bucks/computer/year for home use–or use the software for free to back up to local drives or drives connected to an offsite computer.

Time Machine has its uses, and is definitely "better than nothing", but I use it for recovery of individual files and prefer these other solutions for transferring data to a new computer.