My new iMac with a 2TB hard drive is on the way. Do I have to use a 2tb external hard drive to use time machine or can I go with a smaller one to save money and then upgrade in a few years when the 2tb starts to get filled up?
Depends on how full your 2TB is. TM compresses the files so if you back up e.g. 100GB, it'll use less than 100GB from the external HD as the files are compressed. TM will automatically delete older backups when the HD gets full
Time Machine does not compress files, but not all files on your hard drive will be backed up. Also, since the iMac is brand new, it's doubtful the drive will be full right away (unless you're migrating from another computer/plan on downloading as much as you can in as little time as possible ). As Hellhammer mentioned, when the drive is full, the oldest backups do get deleted, so you'll always have room if you don't mind losing those backups. Plus you can always upgrade to a larger drive if you find yourself requiring the backup space.