To help my mom understand how time machine worked I sent her
this guide (pdf).
Basically, you want a hard drive, it can be dedicated to time machine (recommended but not necessary) or partitioned to be dedicated to both file storage and time machine backups.
I just got a WD Passport and partitioned it so that 120 gb was for time machine and the rest was for file storage.
Read the guide, but it's real simple. The second you hook up an external hard drive you will actually be asked if you want to use it as a TM backup disk. I say no so I can allocate specific space and such, but that is just me.
Since this is for my Air I'll just keep it backed up every so often. I'll keep a second TM backup to a networked drive when I am home, it'll backup wirelessly. The purpose of using the portable is in the event I am away from my home network, I can backup every so often and not worry too much.
Check the guide, if it doesn't make sense lemme know.
One more thing, you can exclude files from the backup. I exclude music since it is already stored and backed up from my NAS.